Please help! Quadratic equation

Question

A rectangle has dimensions x + 10 and 5x-4 where x is in centimetres. If the area of the rectangle is 72 cm², what is the value of x, to the nearest tenth of a centimetre?

Answer 1

Hi Scott,

The area of a rectangle can be determined by multiplying the width times the length:

A = w • l

Here the width would be represented (5x - 4) and the length as (x+10) with the area given as 72

72 = (5x - 4) ( x + 10)

Now we can multiply the terms and find the value of x as follows:

72 = 5x² + 50x - 40

72 - 72 = 5x² + 50x - 40 - 72

0 = 5x² + 50x - 112

This factors to 0 = (5x + 56) (x -2)

x = -56/5 OR x = 2

Since x can not be this large of a negative number because the length and width would be negative, the solution for x would be; x= 2

Therefore, the width is 5x - 4 = 5 • 2 - 4 = 6 cm

The length will be x + 10 = 2 + 10 = 12 cm