Question

The lenght is (x+3) and the width is (x+2). Find the perimeter if the Area is 90.

A. 58
B. 48
C. 38
D. 28

Answer 1

The area of the rectangle is given by:

Area = Length x Width

Substituting the given values, we get:

90 = (x+3)(x+2)

Expanding the right side:

90 = x^2 + 5x + 6

Rearranging the terms:

x^2 + 5x - 84 = 0

Factoring the quadratic equation:

(x + 12)(x - 7) = 0

Therefore, x = -12 or x = 7. Since the length and width cannot be negative, we take x = 7.

So, the length is (x+3) = 10 and the width is (x+2) = 9.

The perimeter of the rectangle is given by:

Perimeter = 2(Length + Width)

Perimeter = 2(10 + 9)

Perimeter = 2(19)

Perimeter = 38

Therefore, the answer is (C) 38.

Explanation: