8x + 2y = 80
4x + 2y = 52

  ( 7 , 12 )    x = 7, y = 12

Step-by-step explanation:

use the method of elimination

    8x + 2

-   4x + 2y = 52

    4x = 28

     x = 7

plug it back into one of the original equations

8x + 2y = 80

8(7) + 2y = 80

56 + 2y = 80

2y = 24

y = 12

(7, 12)

(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