Question

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

Answer 1

Answer:

$L = 6$ --- Length

$W = 4.5$ --- Width

Step-by-step explanation:

Given

Let: $L = Length; W = Width$

$Area = 27m^2$

$L = 2W- 3m$

Required

Find the dimensions of the rectangle

Area (A) is calculated as:

$A = L * W$

This gives:

$27 = (2W - 3) * W$

Open bracket

$27 = 2W^2 - 3W$

Express as a quadratic function

$2W^2 - 3W - 27 = 0$

Expand

$2W^2 + 6W - 9W - 27 = 0$

Factorize:

$2W(W + 3) - 9(W + 3) = 0$

$(2W - 9)(W + 3) = 0$

This gives:

$2W - 9 = 0\ or\ W + 3 = 0$

$2W = 9 \ or\ W = -3$

Width can not be negative.

So:

$2W = 9$

$W = 4.5$

Recall that:

$L = 2W- 3m$

$L = 2 * 4.5 - 3$

$L = 6$