Question

The bases of Triangle A and Triangle B are equal. The ratio of the height of Triangle A to the height of Triangle B is 4:5. If the height of Triangle A is 16 cm and its base is 12 cm, what is the area of Triangle B?​

Answer 1

Answer:

A = 120 cm²

Step-by-step explanation:

The 4 part of the ratio relates to the height of triangle A , then

16 ÷ 4 = 4 cm ← value of 1 part of the ratio, then

5 parts = 5 × 4 cm = 20 cm

The area (A) of triangle B is calculated as

A = $\frac{1}{2}$ bh ( b is the base and h the height )

Here b = 12 and h = 20 , then

A = $\frac{1}{2}$ × 12 × 20 = 6 × 20 = 120 cm²

Answer 2

The height of the triangle is 20 and the area of the triangle B is 120 cm^2

Area of the triangle:

The area of the triangle can be calculated as

Area = $\frac{1}{2}*base*height$

How to find area of the triangle?

Here we have given that

The base of the triangle A = The base of the triangle B = 12 cm

The ratio of the height of triangle A to triangle B is = 4/5

And the height of the triangle A is = 16 cm

If x is the height of the triangle B then

$\frac{16}{x}=\frac{4}{5}$

4x = 80

x = 20

Therefore the height of the triangle B is 20 cm

Now substitute these values in the above formula we have

Area of triangle B = 1/2 x 12 x 20

Area of triangle B = 120 cm^2

Hence the final answer is 120 cm^2

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