In the figure, the ratio of the perimeter of rectangle abde to the perimeter of triangle bcd is . the area of polygon abcde is square units.

choices for the first blank.
a: 2/3
b: 1
c: 3/2
d: 2

choices for the second blank
a: 18
b: 22
c: 24
d: 28

Step 1

Find the perimeter of rectangle ABDE

we know that

the perimeter of rectangle is equal to

In this problem

substitute

Step 2

Find the perimeter of triangle BCD

we know that

the perimeter of triangle is equal to

In this problem we have

Applying the Pythagoras theorem

substitute

Find the ratio of the perimeter of rectangle ABDE to the perimeter of triangle BCD

we have

the perimeter of rectangle is equal to

the perimeter of the triangle is

so

the ratio is equal to

therefore

the answer Part 1) is the option B

Step 3

Find the area of polygon ABCDE

we know that

The area of polygon is equal to the sum of the area of rectangle plus the area of triangle

Area of rectangle is equal to

Area of the triangle is equal to

the height h of the triangle is equal to

substitute

The area of polygon is

therefore

the answer part 2) is the option C

15 units use socratic

step-by-step explanation: 15 units

360/29

step-by-step explanation: