Question

A projector displays an image on a wall. The area (in square feet) of the projection is represented by x^2-8x+15

a. write a binomial that represents the height of the projection
b. find the perimeter of the projection when the height of the wall is 8 feet​

Answer 1

• a. (x - 5) ft
• b. 16 ft

Explanation:

The area given:

• x² - 8x + 15

a. The height is the factor of the area:

• x² - 8x + 15 =
• x² - 3x - 5x + 15 =
• x(x - 3) - 5(x - 3) =
• (x - 3)(x - 5)

The width is x - 3, so the height is x - 5

b. The perimeter formula:

• P = 2(x - 3 + x - 5) = 2(2x - 8) = 4x - 16

The height of the wall is 8 ft:

• x = 8

The perimeter is:

• P = 4*8 - 16 = 32 - 16 = 16 ft