138k views
4 votes
the perimeter of pentagon A is 15 in. Its area is 30 in^2. The perimeter of pentagon B is 25 in. What is the area of pentagon B assuming that these pentagons are similar

User Pescuma
by
8.6k points

1 Answer

3 votes

Answer:

The area of pentagon B is
83(1)/(3)\ in^(2)

Explanation:

step 1

Find the scale factor

we know that

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

Let

z-----> the scale factor

x----> perimeter pentagon B

y----> perimeter pentagon A


z=(x)/(y)

substitute the values


z=(25)/(15)

Simplify


z=(5)/(3) ----> scale factor

step 2

Find the area of pentagon B

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 pentagon B

y----> area pentagon A


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

we have


z=(5)/(3)


y=30\ in^(2)

substitute and solve for x


((5)/(3))^(2)=(x)/(30)


((25)/(9))=(x)/(30)


x=30*((25)/(9))=83.33\ in^(2)

convert to mixed number


83.33=83(1)/(3)\ in^(2)

User ZombieSheep
by
7.0k points