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
devlian [24]
3 years ago
10

What length is the shorter leg of a right triangle that has hypotenuse 50 in long and its perimeter is 112 inches?

Mathematics
2 answers:
Brut [27]3 years ago
8 0
The length of the shorter leg is 14 inches.

We will set up two equations for this; first, for the perimeter.  We will call the legs a and b:

a + b + 50 = 112

Subtract 50 from both sides:
a + b + 50 - 50 = 112 - 50
a + b = 62

We will isolate a, so we can use substitution.  Subtract b from both sides:
a + b - b = 62 - b
a = 62 - b

Now we will set up our Pythagorean theorem equation:
a² + b² = 50²
a² + b² = 2500

We will substitute our value for a from the first equation into this one:
(62-b)² + b² = 2500
(62 - b)(62 - b) + b² = 2500

Multiplying the binomials, we have:
62*62 - b*62 - b*62 -b(-b) + b² = 2500
3844 - 62b - 62b + b² + b² = 2500

Combining like terms:
3844 - 124b + 2b² = 2500

To set it equal to 0 and solve, we subtract 2500 from both sides:
3844 - 124b + 2b² - 2500 = 2500 - 2500
1344 - 124b + 2b² = 0

In standard form, we have
2b² - 124b + 1344 = 0

Using the quadratic formula, 
\frac{--124\pm \sqrt{(-124)^2-4(2)(1344)}}{2(2)}
\\
\\=\frac{124\pm \sqrt{15376-10752}}{4}
\\
\\=\frac{124\pm \sqrt{4624}}{4}=\frac{124\pm 68}{4}=\frac{124+68}{4}\text{ or }\frac{124-68}{4}
\\
\\=\frac{192}{4}\text{ or }\frac{56}{4}=48\text{ or }14

The shorter leg is 14 and the longer one is 48.
Jet001 [13]3 years ago
6 0

Answer:

14

Step-by-step explanation:

Pythagorean triple: {7, 24, 25}

Hypotenuse = 50

50 = 25*2

So, the two other legs are 7*2 = 14 and 24*2 = 48

We can confirm this by adding 14 + 48 + 50 = 112

You might be interested in
(2x^3+10x^2)/(x^2+x-20) divided by (2x^2)/(x-4)
Nutka1998 [239]

Answer:

1

Step-by-step explanation:

Who knew the answer would be 1 LOL

hope this helps :)

8 0
3 years ago
When inscribing a square in a circle, which of these should have equal lengths? A) a radius of the circle and a diagonal of the
koban [17]
Hope this helps you.

5 0
3 years ago
Read 2 more answers
Fine the average of these numbers, 8,12,13,15
GarryVolchara [31]

Answer:

12

Step-by-step explanation:

The average is calculated as

average = \frac{sum}{count} = \frac{8+12+13+15}{4} = \frac{48}{4} = 12

8 0
3 years ago
Read 2 more answers
No one will answer this probably wasting my points XD) Spunky the terrier is chasing a chicken. Spunky runs at a rate of r feet
Vesna [10]
It sucks that points have to be used in order to post questions. 

Openstudy - the company that merged into Brainly -  was much better.

Anyway, I think that the answer to this question is A. I'm not sure, though.
4 0
2 years ago
Re-write the quadratic function below in Standard Form y=-2(x-6)^2-3
Marat540 [252]

Answer:

Step-by-step explanation:

y=−2x2+24x−75

8 0
3 years ago
Other questions:
  • Which of the relations given by the following sets of ordered pairs is a function?
    6·1 answer
  • What information do you need to know in order to find the surface area of a rectangular prism
    6·1 answer
  • Which function is graphed below
    14·2 answers
  • 24% of 1321 is how much? round the answer to the nearest hundredth
    5·2 answers
  • How do you write the equation in slope-intercept form of the line that has a slope of 2 and contains the point (1,1)
    10·2 answers
  • Distributive Property 1 <br><br> 2(x+3)<br><br> What is the answer
    15·2 answers
  • Let f(x) = x2 − 81. Find f−1(x).
    11·1 answer
  • Please help me thanks please
    7·1 answer
  • Please help! I get how to do the first part I just don't get how to do the second part.
    10·1 answer
  • Hello! I'm in the 7th grade and I'm having trouble with math this year... Will someone please help me with this? :)
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!