Question

Use the given area to find stuff

A. 13.5 in.
B. 15 in.
C. 22.5 in.
D. 25 in.

Answer 1

Option B.
`XY=15\ in`

Explanation:

step 1

Find the scale factor

we know that

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

Let

z----> the scale factor

x----> area of the larger pentagon (UVWXY)

y----> area of the smaller pentagon (LMNPO)

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

we have

`x=198\ in^(2)`

`y=88\ in^(2)`

substitute

`z^(2)=(198)/(88)`

`z^(2)=2.25`

`z=1.5`

step 2

Find XY

we know that

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

Let

z----> the scale factor

x----> side XY of the larger pentagon (UVWXY)

y----> side OP of the smaller pentagon (LMNPO)

`z=(x)/(y)`

we have

`z=1.5`

`y=10\ in`

substitute

`1.5=(x)/(10)`

`x=1.5*10=15\ in`

therefore

`XY=15\ in`