\( hw=315\\ h=w+6\\ (w+6)w=315\\ w^2+6w-315=0\\ w^2+21w-15w-315=0\\ w(w+21)-15(w+21)=0\\ (w-15)(w+21)=0\\ w=15 \vee w=-21\\\\ h=15+6=21\\\\\ w=15 \ in\\ h=21\ in\\ \)

*Answer:*

length of window = 21 in

width of window = 15 in*Explanation:*

Assume that the width of the window is w

We are given that the length is 6 in longer than the width

This means that:

length of window = w + 6

Area of rectangle is calculated as follows:

area = width * length

area = w(w+6)

315 = w(w+6)

315 = w² + 6w

w² + 6w - 315 = 0

(w-15)(w+21) = 0

This means that:

either w-15=0.> w = 15 in. > accepted solution

or w+21 = 0.> w = -21 in. > rejected as width of window cannot be negative

Now, we know that:

length = width + 6

length = 15 + 6

length = 21 in

Based on the above calculations:

length of window = 21 in

width of window = 15 in