Question

The area of a rectangular field is given by the trinomial t2 – 4t – 45. The length of the rectangle is t + 5. What is the expression for the width of the field?

Answer 1

The answer is: width = t - 9

A = l * w
A = t² - 4t - 45
l = t + 5
t² - 4t - 45 = (t + 5)w

$w= \frac{ t^{2} - 4t - 45}{t + 5} = \frac{t * t - 9t + 5t - 5 * 9}{t+5} = \frac{t(t - 9) + 5(t - 9))}{t+5} = \frac{(t-9)(t+5)}{t+5} =t-9$