Question

The length of a rectangle is 5 cm longer than its width. find the width given that the area is 36cm

Answer 1

Hi there! The answer is 4 cm.

Let the width of the rectangle be represented by X.
Now we can conclude we can express the length by X + 5.

The area of a rectangle can be found using the formula:
A = W × L = width × length.

Filling in the formula gives us the following:

`x(x + 5) =`

Work out the parenthesis (for instance using rainbow technique).

`{x}^(2) + 5x`

Now, when we've found our expression that represents the area, we can set up and solve an equation.

`{x}^(2) + 5x = 36`

Subtract 36.

`{x}^(2) + 5x - 36 = 0`

Factorise

`(x + 9)(x - 4) = 0`

Rule AB = 0, gives A = 0 or B = 0

`x + 9 = 0 \\ x = - 9 \\ or \\ x - 4 = 0 \\ x = 4`

Since length can't be negative, the width of the rectangle, which was represented by x, is 4.
The answer is 4 cm.

~ Hope this helps you!