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!