The length of a rectangle is 7 centimeters less than twice the width. If the area of the rectangle is 165 square centimeters, find the length and width

Answer 1

Hi, David,

For problems like this, start by writing down what you know. In this case A = L x W

Since you don't know the length and width, write algebraic expressions for each:

Let x = width

Then 2x-7 = length (7 less than twice the width)

Now plug everything into the area formula:

A = L x W

165 = x(2x-7)

165 = 2x²-7x (distributive property)

Now solve the resulting quadratic equation:

This will factor to:

(2x+15)(x-11) = 0

The resulting roots are x = 11 and x = -15/2

The negative root makes no sense, since distances can't be negative, so the correct value is 11, which is the width.

Plug this into your expression for length

L = 2x-7

L = 2(11) -7

L = 22-7

L = 15

Check the answer by testing whether W = 11 and L = 15 gives you the area of 165 cm²

Best wishes!

Answer 2