The area of a bulletin board is 52squarefeet. The length is three feet less than four times the width. Find the length and the width of the bulletin board.

width = 4ft

length = 13

Step-by-step explanation:

Let the unknown value of width be y; and the unknown value of length be x

4 times the width = 4y

The length, x is 3 feet less than 4y

=

A board is rectangular in shape.

The formula for calculating the area of a rectangle is;

Area= width x length

Area of the bulletin board is given as 52 ft²

Width = y

Length = 4y - 3

Therefore,

This leads to a quadratic equation which has the form

Steps to solving a quadratic equation are

1. Multiply the coefficient of x² by c, i.e, a times c =

2. We look for two factors of ac that can also be added together to give b.

corresponds to

4 x -52 = -208

Two factors of -208 that can add up to give -3 are -16 and 13

We can write as

We factorise each brackets

This becomes,

Or

A quadratic equation has two solutions. Therefore, or

But the width of a rectangle is usually a natural number hence, the possible value of the width y, is = 4

Length,

but y = 4

Therefore length, x=