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

Answer:

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

Step-by-step 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.