Question

Ashwin helps paint a square mural in his classroom. Then he helps paint a mural in the hallway whose length is 7 feet longer and whose width is 3 feet shorter. Let x represent the side length of the mural in Ashwin's classroom. Write an expression that represents the two binomials you would multiply to find the area of the hallway mural. Use that expression to find the area of the hallway mural if each side of the classroom mural is 8 feet long.

A.
(x + 7)(x + 3); 165 square feet

B.
(x – 7)(x + 3); 11 square feet

C.
(x – 7)(x – 3); 5 square feet

D.
(x + 7)(x – 3); 75 square feet

Answer 1

(x + 7)(x - 3) = 75 square feet.

Explanation:

Given that x represents the side length of the mural in Ashwin's classroom, the hallway mural's length is x + 7 feet and its width is x - 3 feet. The area of the hallway mural can be found by multiplying these two binomials, (x + 7)(x - 3), to get x^2 + 4x - 21.

If each side of the classroom mural is 8 feet long, the hallway mural would have sides of 15 feet and 5 feet, so its area would be 75 square feet, which is the answer.