If a storm windows has an area of 315 square inches, what are the dimensions if the window is 6 inches higher than it is wide (w x h)

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

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


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