Question

A projector displayed a rectangular image on a wall. the height of the wall is x feet. the area (in square feet) of the projection is represented by x² - 12x + 32. the width of the projection is (x-4) feet.

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 10 feet.

Answer 1

The height of the projection represented by the binomial is (x-8) feet. The perimeter of the projection when the wall height is 10 feet is 16 feet.

Step-by-step explanation:

To find the binomial that represents the height of the projection when the area is given by x² - 12x + 32 and the width is (x-4) feet, we divide the area by the width:

Height = ²area / width

= (x² - 12x + 32) / (x - 4)

Applying polynomial division or factoring, we find the height of the projection is (x-8) feet.

For part b, the perimeter of the projection when the wall height is 10 feet is calculated by:

Perimeter = 2 × height + 2 × width

= 2 × (10 - 8) + 2 × (10 - 4)

= 2 × 2 + 2 × 6

= 4 + 12

= 16 feet.