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.

Question

Mathematics

Julia

14 January, 10:23

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.

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Answers (1)

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Isaac Conrad · 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.