Question

A rectangle has a length that is 8 inches more than its width, w. The area of the rectangle is 65 square inches.

(a) Write an expression for the length of the rectangle in terms if its width, w
length=

(b) Using your answer from (a), write an equation that could be used to solve for the width, w, of the rectangle.
Equation:

Answer 1

please see answers below

Explanation:

a) if length, L, is 8 inches more than the width, W, then we can say

L = W + 8.

b) L X W = 65

(W + 8) X W = 65

W² + 8W = 65

subtract 65 from both sides:

W² + 8W - 65 = 0.

we can use completing the square, quadratic formula or factorisation to solve.

I will use completing the square.

1) put the W, not W ², in parenthesis.

2) half the coefficient (8) of W. that is 4. Put that into same parenthesis. Square the parenthesis.

3) we have (W + 4)²

4) Subtract (+4) ² = 16 from this.

5)[(W + 4) ² - 16] – 65 = 0

6) now we have (W + 4) ² – 81 =0

7) (W + 4) ² = 81

8) (W + 4) = ± √81

9) W = ± √81 - 4

10) W = ±9 - 4. W = -13 or W = 5.

lengths are widths are positive, so W must be positive. So we choose 5.

L = W + 8 = 5 + 8 = 13.

check if it works for the area of 65.

L X W = 13 X 5 = 65.

so length is 13 inches and width is 5 inches