1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ElenaW [278]
3 years ago
7

A right triangle's hypotenuse is 10 inches long. The length of one leg of a right triangle is 2 inches more than the second leg.

What are the lengths of the legs of the triangle?

Mathematics
2 answers:
zhannawk [14.2K]3 years ago
8 0

Answer:

  8 inches and 6 inches

Step-by-step explanation:

The hypotenuse length of 10 is 2 times 5, so there is a possibility that the triangle is a 3-4-5 triangle scaled by a factor of 2. The leg length difference of 2 confirms this. The right triangle of interest has sides of 6 inches, 8 inches, and 10 inches, double the sides of a 3-4-5 triangle.

Since "one leg" is 2 inches longer, it must be the 8-inch leg. The "second leg" must be the 6-inch leg.

_____

The 3-4-5 right triangle shows up in many algebra and geometry problems, so is useful to remember.

If you want to solve this algebraically, you can assign x as the length of "one leg" and (x -2) as the length of "the second leg." Then the Pythagorean theorem tells you ...

  10² = x² +(x -2)²

  100 = 2x² -4x +4

  x² -2x -48 = 0 . . . . . subtract 100, divide by 2

  (x -8)(x +6) = 0 . . . . .factor

  x = 8 . . . . . . . . . . . . . the positive solution; the only one of interest

One leg is 8 inches; the second leg is 6 inches.

Paul [167]3 years ago
3 0

6 inches and 8 inches.

<h3>Further explanation</h3>

<u>Given:</u>

  • A right triangle's hypotenuse is 10 inches long.
  • The length of one leg of a right triangle is 2 inches more than the second leg.

<u>Question:</u>

What are the lengths of the legs of the triangle?

<u>The Process:</u>

We will solve a problem regarding right triangles. In the process, there is a relationship between the Pythagorean Theorem with Quadratic Equations.

Let x as the length of one leg of a right triangle. Thus, the length of the second leg is (x - 2).

All length units were expressed in inches.

Let us find out the lengths of the legs of the triangle.

The Phytagorean Theorem: \boxed{ \ (leg)^2 + (leg)^2 = (hypotenuse)^2 \ }

\boxed{ \ (x-2)^2 + (x)^2 = (10)^2 \ }

Remember this, \boxed{\boxed{ \ (a - b)^2 = a^2 - 2ab + b^2\ } \ \boxed{ \ (a +b)^2 = a^2 + 2ab + b^2\ }}

\boxed{ \ x^2 - 4x + 4 + x^2 = 100 \ }

\boxed{ \ 2x^2 - 4x + 4 - 100= 0 \ }

\boxed{ \ 2x^2 - 4x - 96= 0 \ }

Divide by two on both sides.

\boxed{ \ x^2 - 2x - 48= 0 \ }

\boxed{ \ (x - 8)(x + 6) = 0 \ }

  • The accepted root represents x = 8 inches long because the length must be positive.
  • Thus, the length of the second leg is 8 - 2 = 6 inches long.

- - - - - - - - - -

Notes

Of course, we agree with the use of the right intuition, which is to remember Pythagorean Triples, i.e., \boxed{ \ 3-4-5 \ } \rightarrow \boxed{ \ 6-8-10  \ } This method is very convenient when working on multiple-choice tests in a limited amount of time.

<h3>Learn more</h3>
  1. Find out the measures of the two angles in a right triangle brainly.com/question/4302397
  2. A word problem of a quadratic equation brainly.com/question/11805547
  3. What is the area of triangle ABC ? brainly.com/question/4206319

You might be interested in
Need help in number 12 and 13 PLEASEE!! I don’t get it and I start school the day after tomorrow
Natasha_Volkova [10]

Answer:

The explanations for the graphs are provided down below. Please let me know if you have any questions about my answer.

12 and 13 as written on the worksheet is right.

Step-by-step explanation:

12) The answer given is correct.

The relation between x and y is given as:

y=\frac{x^2}{2}-3 with x \in \{-4,-2,0,2}.

I replaced the word domain with x since the domain is the set of x's for which the relation exists.

We are going to replace x with each of the x's given to see what y corresponds to each.

Let's begin with x=-4.

y=\frac{x^2}{2}-3 with x=-4:

y=\frac{(-4)^2}{2}-3

y=\frac{16}{2}-3

y=8-3

y=5.

So (-4,5) is an ordered pair that should be on our graph.

To find this point you move left 4 from origin then up 5. Now you put a dot where you have landed. Your graph does show this point.

Moving on.

Let's do the next x: x=-2.

y=\frac{x^2}{2}-3 with x=-2:

y=\frac{(-2)^2}{2}-3

y=\frac{4}{2}-3

y=2-3

y=-1.

So (-2,-1) is an ordered pair that should be on our graph.

To find this point you move left 2 from origin and then down 1.  Now you put a dot where you have landed. Your graph shows this point as well.

Now x=0.

y=\frac{x^2}{2}-3 with x=0:

y=\frac{0^2}{2}-3

y=\frac{0}{2}-3

y=0-3

y=-3

So (0,-3) is an ordered pair that should be on our graph.

To find this point you move left and right none and down 3.  Now you put a dot where you have landed. Your graph shows this point.

Now the last point will be at x=2.

y=\frac{x^2}{2}-3 with x=2

y=\frac{2^2}{2}-3

y=\frac{4}{2}-3

y=2-3

y=-1.

So (2,-1) is an ordered pair that should be on our graph.

To find this point you move 2 units right from the origin and then down 1 unit. Now put a dot where you landed.  The graph shows this point as well.

13) The answer given is correct.

g(x)=|x| is the parent function and makes like a V shaped graph where it's vertex is at (0,0).

If we want to move this graph right 3 it becomes:

m(x)=|x-3| \text{ or } m(x)=|(-1)(-x+3)|=|-1||-x+3|=1|-x+3|=|-x+3|=|3-x|.

If you move that up once it becomes:

n(x)=|x-3|+1 or n(x)=|3-x|+1 which is the curve given.

If you don't know about transformations you can choose a few points to plug in to see what's going on with the graph.

Let's choose x=-5,-3,-1,0,1,3,5.

x=-5

f(-5)=|3--5|+1=|3+5|+1=|8|+1=8+1=9.

There is no room for (-5,9) on our graph but if you extended the left hand side of the absolute value function there you would see that (-5,9) is reached.

x=-3

f(-3)=|3--3|+1=|3+3|+1=|6|+1=6+1=7.

(-3,7) should be a point on the graph. Same thing for this point as (-5,9).

x=-1

f(-1)=|3--1|+1=|3+1|+1=|4|+1=4+1=5.

(-1,5) is located on the graph.

x=0

f(0)=|3-0|+1=|3|+1=3+1=4.

(0,4) is also located on the graph.

x=1

f(1)=|3-1|+1=|2|+1=2+1=3.

(1,3) is located on the graph.

x=3

f(3)=|3-3|+1=|0|+1=0+1=1.

(3,1) is located on the graph.

x=5

f(5)=|3-5|+1=|-2|+1=2+1=3.

(5,3) is located on the graph.

Now if we weren't given the graph already:

I would plot the points I found which were:

(-5,9)

(-3,7)

(-1,5)

(0,4)

(1,3)

(3,1)

(5,3)

We should get a basic idea of what the function looks like from these points.

I will graph them. You will have to connect these points because the domain isn't discrete like number 12 is.  That is they didn't list out elements for the domain.

I'm going to graph one more point after x=5.

How about x=7?

f(7)=|3-7|+1=|-4|+1=4+1=5

So (7,5) is also a point on the graph.

You should see that the blue points are following the red path I made there.

8 0
3 years ago
A small bar of gold measure 40 mm by 25 mm. by 2 mm. Find the volume in cubic millimeters.
vladimir2022 [97]

Answer:

2000 mm^3* .0005oz/1mm^3=1oz

Step-by-step explanation:

v=40mm*25mm*2mm=2000mm^3

7 0
3 years ago
Read 2 more answers
What is the answer to -5 ( 4w +12) =15 make sure you write the answer as a decimal
seropon [69]

Answer:

w= -3.75

Step-by-step explanation:

-5(4w+12) =15

-20w -60=15

-20w=75

w=-3.75

8 0
3 years ago
Read 2 more answers
Help please it says choose all answers that apply
Anestetic [448]

Answer:

x = 1

x = 0

x = 1 1/4

Step-by-step explanation:

x = 1

x = 0

x = 1 1/4

The < sign means less than. -1/4 is less than 1, 0, and 1/4, and more than -3/4 and -1. So, 1, 0, and 1 1/4 are the right answers.

<em>Hope that helps!</em>

<em>-Sabrina</em>

8 0
3 years ago
A bookcase has a mass of 20 kilograms. A book in the bookcase has a mass of 500 grams.
dimaraw [331]

Answer:

Step-by-step explanation:

Remark

You have to convert one of the numbers. It doesn't matter which one, but you can't simply divide one into the other the way the numbers stand.

Conversion

20 kilograms = 20 * 1000 grams / kg

20 kilograms = 20000 grams

Formula

Number of books = mass of bookcase / mass of 1 book

Givens

number of books = ??

mass of bookcase = 20000 grams

mass of one book = 500 grams

Solution

number of books = 20000 / 500

number of books = 40

Answer: 40 books =  mass of bookcase

6 0
2 years ago
Other questions:
  • What is a cubic polynomial function in standard form with zeros 1,1,and -3?
    5·1 answer
  • If x + 9.8 = 14.7, what is the value of 8(x - 3.7)?
    11·2 answers
  • They ratio of pencils to erasers is 4:1 if their are 20 pencils how many erasers are there
    9·1 answer
  • Please help! I have this question and one more I'm about to post, if you can answer them that would be most appreciated. These a
    6·1 answer
  • Find the mean for the group of data items. Round to the nearest hundredth, if necessary.
    14·1 answer
  • Which ordered pair is the solution to the system of linear equations y=5x+8 and -4x-1 ?
    12·2 answers
  • Answer the question
    13·1 answer
  • What is the solution to f (x)=g (x), if f (x)=-x and g (x)=x​
    11·1 answer
  • Really need help! anything would be appreciated
    10·2 answers
  • Plz help. <br> It’s algebra
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!