Question

PLsss help 15 points!

In the figure below, △ABC ~ △PQR. If the Area of △ABC is 40 cm2, what is the area of △PQR? show your work.

Answer 1

The area of △PQR is
`90\ cm^(2)`

Explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

so

Let

z-----> the scale factor

x---> the corresponding side triangle PQR

y---> the corresponding side triangle ABC

`z=(x)/(y)`

substitute the values

`z=(6)/(4)=1.5`

step 2

Find the area of triangle PQR

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

so

Let

z-----> the scale factor

x---> the area of triangle PQR

y---> the area of triangle ABC

`z^(2) =(x)/(y)`

we have

`z=1.5`

`y=40\ cm^(2)`

substitute the values

`1.5^(2) =(x)/(40)`

`x=40(1.5^(2))=90\ cm^(2)`

Answer 2

90 square cm.

Explanation:

For similar figures, the length of corresponding sides are proportional.

So we can write 4k = 6 where k is the proportionality constant.

Note: In terms of area, the scale factor would be k^2 and in terms of volume, it would be k^3y

Solving 4k = 6, we see that k = 6/4 or 3/2

We need area, so we multiply area of ABC by k^2 to get area of PQR.

`40((3)/(2))^2\\=40((9)/(4))\\=90`

Area of PQR = 90 cm^2