Question

The length of a rectangle is 1 unit more than the width. The area of the rectangle is 56 units. What is the width in units of the rectangle

Answer 1

Answer:

Width = 7units

Step-by-step explanation:

The area of a rectangle

A = h * w

A - area of a rectangle

h - height of a rectangle

w - width of a rectangle

Or

A = length * breadth

It's all the same

Given :

h = 1 + w

w = w

A = 56

56 = ( 1 + w) * w

56 = ( 1 + w)w

56 = w + w^2

56 = w^2 + w

w^2 + w - 56 = 0

Find a factor that can be multiplied to give -56

and added to give + 1

The factor is 8 and -7

Substitute 8w - 7w for w

w^2 + 8w - 7w - 56 = 0

( w^2 + 8w) - (7w - 56) = 0

w( w + 8) - 7( w + 8) = 0

( w - 7) = 0

( w + 8) =0

w - 7 = 0

w = 7

w + 8 = 0

w = -8

Since a side of any rectangle can not be negative

w = 7

The width of the rectangle is 7units

The length of the rectangle is 1 + w = 1 + 7 = 8units