# The length of a rectangle is 3 inches longer than twice its width, where w is the width of th rectangle. The area of the rectangle is

Question

The length of a rectangle is 3 inches longer than twice its width, where w is the width of th
rectangle. The area of the rectangle is 90 square inches. *

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1 year 2021-09-03T23:34:27+00:00 2 Answers 8 views 0

1. ASSUMPTION:

Let width be x, then length be 2x + 3.

GIVEN:

• Area of rectangle = 90in²

We know that,

Area of rectangle = lw

• x(2x + 3) = 90
• 2x² + 3x – 90 = 0

So, x = – 3 ± √3² – 4 × 2 × – 90/2 × 2

• x = – 3 ± √729/4
• x = – 3 ± 27/4
• x = 6 (width can’t be negative)

Then, length = 2 × 6 + 3 = 15in.

Hence, length of rectangle is 15in and width is 6in.

• 6 in and 15 in

Step-by-step explanation:

Given:

• l = 2w + 3
• A = 90 in²
• w = ?
• l = ?

Area formula:

• A = lw

Substitute values and solve for w:

• (2w+3)w = 90
• 2w² + 3w = 90
• 2w² + 3w – 90 = 0
• w = (-3 ± $$\sqrt{3^2 – 4*2*(-90)}$$)/2*2
• w = (-3 ± √729)/4
• w = (-3 ± 27)/4
• w = 6 (positive root only)

The width is 6 in, find the length:

• l = 2*6 + 3 = 15 in