Question

A carpenter is putting a skylight in a roof. If the roof measures 10 + 8 by 8 + 6 and the skylight measures + 5 by 3 + 4, what is the area of the remaining roof after the skylight is built?

a. 77^2 + 115 + 68
b. 77^2 + 105 + 28
c. 83^2 + 115 + 68
d. 77^2 − 105 + 28

Answer 1

The area is:
`77x^2 + 105x + 28`, option b.

Explanation:

Rectangular area:

The area of a rectangular space is given bt the multiplication of its measures.

Area of the roof:

Dimensions of 10x + 8 and 8x + 6. So

`A_(r) = (10x+8)(8x+6) = 80x^2 + 60x + 64x + 48 = 80x^2 + 124x + 48`

Area of the skylight:

Dimensions of x + 5 and 3x + 4. So

`A_(s) = (x+5)(3x+4) = 3x^2+4x+15x+20 = 3x^2 + 19x + 20`

What is the area of the remaining roof after the skylight is built?

Total subtracted by the skylight, which is a subtraction of a polynomial, in which we subtract the like terms. So

`A_(r) - A_(s) = 80x^2 + 124x + 48 - (3x^2 + 19x + 20) = 80x^2 - 3x^2 + 124x - 19x + 48 - 20 = 77x^2 + 105x + 28`

The area is:
`77x^2 + 105x + 28`, option b.