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
yanalaym [24]
3 years ago
15

The height of a triangle is 5 cm shorter than its base. If the area of the triangle is 25 cm2, find the height of the triangle.

Mathematics
1 answer:
Olin [163]3 years ago
6 0

Answer:

h = 5\ cm

Step-by-step explanation:

Let's call B at the base of the triangle and call h at the height of the triangle. Then we know that:

The height of a triangle is 5 cm shorter than its base. This means that:

h = B-5.

 The area of the triangle is 25 cm²

By definition the area of a triangle is:

A = 0.5Bh

For this triangle we know that A = 25\ cm^2 and h = B-5. We substitute these values in the equation and solve for B.

25 = 0.5B (B-5)

0.5B ^ 2-\frac{5}{2}B-25 = 0

Now we use the quadratic formula to solve the equation.

For an equation of the form ax ^ 2 + bx + c = 0 the quadratic formula is:

B=\frac{-b\±\sqrt{b^2-4ac}}{2a}

In this case note that:  a=0.5,\ \ b=-\frac{5}{2}\ \ c=-25

Then:

B=\frac{-(-\frac{5}{2})\±\sqrt{(-\frac{5}{2})^2-4(0.5)(-25)}}{2(0.5)}

B=\frac{\frac{5}{2}\±\sqrt{\frac{25}{4}+50}}{1}

B=\frac{5}{2}\±\frac{15}{2}

The solutions are:

B_1=\frac{5}{2}+\frac{15}{2}=10

B_2=\frac{5}{2}-\frac{15}{2}=-5

For this problem we take the positive solution.

B=10\ cm

Now we substitute the value of B in the equation to find the height h

h = 10-5

h = 5\ cm

You might be interested in
Draw and label the final image of △ABC after the given sequence of transformations. Reflect △ABC over the y−axis and then transl
arlik [135]

Answer: The correct option is A.

Explanation:

From the given figure it is noticed that each box in the graph represents the length of 2 units. The coordinates of point A,B and C are (-1,1),(-3,3) and  (-2,4) respectively.

If a point reflects over the y-axis then,

(x,y)\rightarrow(-x,y)

So after reflecting coordinates of point C become,

(-2,4)\rightarrow(2,4)

If a point translated by (a,b), then

(x,y)\rightarrow(x+a,y+b)

So, after reflection over y-axis followed by translation by (2,-2), the coordinate of C are,

(2,4)\rightarrow(2+2,4-2)\\(2,4)\rightarrow(4,2)

Similarly the image of point A and B are (3,-1) and (5,1) respectively.

The image of C after reflection over y-axis followed by translation by (2,-2) is (4,2), which is shown in only graph A, Therefore A is the correct option.

8 0
2 years ago
Find the quotient of 3/4 and 5/6 in its simplest form​
Yuri [45]

Answer:

= 1 R 2

= 1 2/3

Step-by-step explanation:

8 0
3 years ago
Help....................
Serhud [2]

Answer:

A) m=\frac{350}{25}

Step-by-step explanation:

We are trying to find how long it will take Carlos to have $500 TOTAL, so we need to subtract what he already has ($150) to get the value we want to divide by $25 to figure out how many months it will take him to save up the rest. The given answer above is just a simplified way of writing m=\frac{500-150}{25}, if that makes more sense.

3 0
3 years ago
Ramon took a collection of colored tiles from a box. Amelia took 14 tiles from his collection and Keiko took half of those remai
zimovet [89]
From the given, it is stated that after Amelia took 14 out of the box, Ramon took half of those which remained and he had 16 tiles. The number of tiles left after Amelia took hers is equal to twice of 16 which is equal to 32 tiles. 

To determine the number of tiles during the start, we can add the 14 tiles from the calculated 32 tiles.
    
         n = 14 tiles + 32 tiles
                 n = 46 tiles

<em>Answer: 46 tiles</em>
4 0
3 years ago
Read 2 more answers
On a field trip, there are 8 adults and 24 students. What is the ratio of students to the total number of people on the field tr
Marianna [84]
24:32 is the ratio. Just add up he total number and then put the total number of student over the total number of people
6 0
3 years ago
Read 2 more answers
Other questions:
  • I have a 67.84% in my class. I have 8 more assignments that are each worth 10% and 1 exam that is worth 50%. So in total, 9 assi
    9·2 answers
  • Adrian’s recipe for cranberry relish calls for 1 1/4 cups of sugar. He wants to use 1/2 that amount. How much sugar should he us
    15·1 answer
  • Rachel spent $628 more than Samuel if Samuel spent $329 then how much did Rachel spent
    9·2 answers
  • Which of the following ordered pairs represents a solution to the linear inequality y&gt;2x-3?
    11·1 answer
  • What is remainder one as a fraction?
    11·2 answers
  • The hole for support needs to be feet deep. It is currently inches deep. How much deeper must the hole​ be? Use pencil and paper
    6·1 answer
  • A summer camp cookout is planned for the campers and their families. There is room for 200 people. Each adult costs 4, and each
    5·1 answer
  • Graduated containers are used to measure ingredients by weight. true or false
    15·1 answer
  • Answers please. First to answer all of them correctly gets brainliest.
    12·1 answer
  • Ilean works as a welder and web designer. As a welder, she earns $18 per hour. Last week she worked 푥 hours as a welder and her
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!