Question

A rectangle with an area of 24 square units has length x+1 and width 4x-6. find the value of x.

Answer 1

Area = length x width.
24 = (x + 2)(x - 3) = x² - x - 6
x² - x - 30 = 0
(x + 5)(x - 6) = 0
We can eliminate the root x = - 5 because dimensions cannot be negative. So, the only valid answer is x = 6

The length = x + 2 = 6 + 2 = 8 in.
The width = x - 3 = 6 - 3 = 3 in.