Question

A square piece of fabric has an area of (9x2 + 24x + 16) square inches. The length of each side of the fabric is (cx + d) in., where c and d are whole numbers. Find an expression for the perimeter of the piece of fabric. Then find the perimeter when x = 2.
A.An expression for the perimeter is (3x + 4)(3x + 4). The perimeter is 100 inches.
B.An expression for the perimeter is 12x + 16. The perimeter is 40 inches.
C.An expression for the perimeter is 12x + 16. The perimeter is 28 inches.
D.An expression for the perimeter is 3x + 4. The perimeter is 10 inches.

Answer 1

The area is:
 (9x2 + 24x + 16)
 Factoring the area, we can find the length of the sides of the square.
 We have then:
 (3x + 4) ^ 2
 Thus, the length of each side is:
 3x + 4
 Then, the perimeter is given by:
 P = 4 * L
 Where,
 L: square side
 Substituting:
 P = 4 * (3x + 4)
 Rewriting:
 P = 12x + 16
 For x = 2 we have:
 P = 12 (2) +16
 P = 24 + 16
 P = 40
 Answer:
 B.An expression for the perimeter is 12x + 16. The perimeter is 40 inches.