50 POINTS!
a) Write a polynomial for the perimeter of this shape. Simplify the polynomial. (The polynomial is in the photo)

b) Determine the perimeter of the shape when d = 5 m.

a) 4d + 18

b) 38 inches

Step-by-step explanation:

a) The perimeter is simply the sum of all the exterior side lengths.

On the top, we've got d and d + 3.

On the left side, we have 2 and an unknown. However, we do know that this "unknown" + 2 will be the same length as the right side, which is 6. So, we have 2 + unknown = 6; hence, the unknown = 4.

The bottom is the same length as the top two lengths, so it's:

d + (d + 3) = 2d + 3

And, the right side is 6.

Adding these together, we have:

d + (d + 3) + 2 + 4 + d + (d + 3) + 6 = 4d + 18

b) We just need to substitute 5 in for d:

4d + 18

4 * 5 + 18 = 20 + 18 = 38 inches

cant open file sorry!

step-by-step explanation:

(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