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. *

Answer 1

Answer:

• 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

Answer 2

width be x

• Length be 2x+3

Now

• area=Length×Breadth
• x(2x+3)=90
• 2x²+3x=90
• 2x²+3x-90=0

On solving we will get

• x=6[Take positive]

Now

Length=2(6)=3=15in