Question

The length of a rectangle is 3 m less than twice the width, and the area of the rectangle is 27 m. Find the dimensions of the rectangle.​

Answer 1

• 4.5 m and 6 m

---------------------------

Let the length be l and width be w.

Given:

• l = 2w - 3,
• A = lw = 27.

Substitute l and solve for w:

• lw = 27

• w(2w - 3) = 27
• 2w² - 3w = 27
• 2w² - 3w - 27 = 0
• 2w² - 9w + 6w - 27 = 0
• w(2w - 9) + 3(2w - 9) = 0
• (2w - 9)(w + 3) = 0
• 2w - 9 = 0 and w + 3 = 0
• 2w = 9 and w = - 3 (discarded as distance can't be negative)
• w = 4.5

Find the value of l:

• l = 2*4.5 - 3 = 9 - 3 = 6