Question

The figures are similar. Find the area.

The area of △ABC is 15 square cm. The height of △ABC is 5 cm and the height of △DEF is 13 cm. Find the area of △DEF. Round to the nearest square cm if necessary.

Answer 1

The area of triangle DEF is
`101\ cm^(2)`

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=(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)=(x)/(y)`

we have

`z=(13)/(5)`

`y=15\ cm^(2)`

substitute and solve for x

`((13)/(5))^(2)=(x)/(15)`

`x=((169)/(25))(15)`

`x=101\ cm^(2)`