Need !

1. the two polygons are similar, homes ~ brick. the polygons are not drawn to scale.

a. set up a proportion.

b. solve for x showing all your work.

a.  

b. x = 4 (see steps below)

Step-by-step explanation:

Since the two polygons are similar, the sides are proportional to each other.  Using a proportion, you can solve for 'x' using cross-multiplication and division:

Cross-multiply: 15(x + 3) = 21(x + 1)

Distribute:  15x + 45 = 21x + 21

Subtract '15x' from both sides: 15x + 45 - 15x = 21x + 21 - 15x or 45 = 6x + 21

Subtract '21' from both sides: 45 - 21 = 6x + 21 - 21 or 24 = 6x

Divide by 6 on both sides: 24/6 = 6x/6

Solve for x: x = 4

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

the correct answer is $7.38

step-by-step explanation: