The area (in square feet) of the school sign can be represented by 15x2 − x − 2. a. Write an expression that represents the length of the sign. If the height of the sign is (3x+1) ft.

Question

Also what is the perimeter of the sign when x=2

Answer 1

Assuming the sign has a rectangular shape:

A = 15x²-x-2 ft²

If the height is (3x+1)ft then the length is (15x²-x-2) / (3x+1) ft, and because 3x+1 divides evenly into 15x²-x-2, we can carry out that division to simplfy things to length = (5x-2) ft

For the perimeter, just plug in x=2 into the height expression and into the length expression,

then use Perimeter = 2L + 2H:

L = 5x-2 = 5(2)-2 = 10-2 = 8 ft

H = 3x+1 = 3(2)+1 = 7 ft

Perimeter = 2L + 2H = 2(8) + 2(7) = 16+14 = 30 ft