Question

The figures are similar. Find the area.

Answer 1

Answer:

The area of triangle DEF is $101\ cm^{2}$

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its heights is proportional and this ratio is called the scale factor and the ratio of its areas is equal to the scale factor squared

step 1

Find the scale factor

Let

z ----> the scale factor

$z=\frac{13}{5}$ ----> ratio of its heights

step 2

Find the area of triangle DEF

Let

z ----> the scale factor

x ----> the area of triangle DEF

y ----> the area of triangle ABC

so

$z^{2}=\frac{x}{y}$

we have

$z=\frac{13}{5}$

$y=15\ cm^{2}$

substitute and solve for x

$(\frac{13}{5})^{2}=\frac{x}{15}$

$x=(\frac{169}{25})(15)$

$x=101\ cm^{2}$