Question

triangle ABC is similar to triangle DEF. the perimeter of triangle ABC is five times the perimeter of triangle DEF. the area of triangle ABC is 100 square centimeters. what is the area of triangle DEF in square centimerts?

Answer 1

Answer:

The area of triangle DEF is $4\ cm^{2}$

Step-by-step explanation:

Step 1

Find the scale factor

we know that

If triangle ABC is similar to triangle DEF

then

the ratio of their perimeters is equal to the scale factor

Let

x-------> perimeter of triangle ABC

y------> perimeter of triangle DEF

z------> scale factor

$z=\frac{x}{y}$

$x=5y$ ------> equation A

Substitute equation A in the formula of the scale factor

$z=\frac{5y}{y}$

$z=5$

Step 2

Find the area of the smaller triangle DEF

we know that

The ratio of the area triangle ABC divided by the area of triangle DEF is equal to the scale factor squared

Let

r------->area of triangle ABC

s------> area of triangle DEF

z------> scale factor

$z^{2}=\frac{r}{s}$

In this problem we have

$z=5, r=100\ cm^{2}$

substitute and solve for s

$5^{2}=\frac{100}{s}$

$s=\frac{100}{5^{2}}$

$s=4\ cm^{2}$

Answer 2

20. because 100/5=20cm2