If a storm window has an area of 400 square inches what are the dimensions if the window is 12 inches higher than it is wide?

Answer 1

This answer for each dimension is provided to 4 decimal places only.

The height of the window is 26.8806 inches and the width is 14.8806 inches.

For, let h equal the height and w the width.

Thus in inches:

1. h * w = 400

2. h - w = 12

We can rewrite 2. as h = w + 12

Substituting h = w + 12 into 1. gives

3. w (w + 12) = 400 thus

w2 + 12w = 400

w2 + 12w - 400 = 0

Substituting the above values into the quadratic formulawhere the roots of aw2 + bw + c = (-b + or - ((b2 - 4ac) 1/2)) / 2a gives:

w = (-12 + or - (122 - (4 * 1 * -400)1/2)) / 2 * 1

= (-12 + or - (144 - -1600)1/2) / 2

= (-12 + or - 17441/2) / 2

= 14.8806 (to 4 decimal places only) and -26.8806(to 4 decimal places only)

We can clearly discount the negative root. Therefore the width of the window is equal to 14.8806 inches (to 4 decimal places only).

Substituting w = 14.8806 into 1. gives

14.8806 * h = 400

h = 400/14.8806

h = 26.8806 (to 4 decimal places)