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Q: If a storm window has an area of 400 square inches what are the dimensions if the window is 12 inches wider than it is high (w x h)?
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area = width times height x = height x-12 = width x (x-12) = x^2 - 12X = 400 x^2 - 12X - 400 = 0 solve for x using quadratic formula X = (12 + SQRT(144 + 1600)) divided by 2 x = 26.88 = height width = x -12 = 14.88


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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?

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 = 4002. h - w = 12We can rewrite 2. as h = w + 12Substituting h = w + 12 into 1. gives3. w (w + 12) = 400 thusw2 + 12w = 400w2 + 12w - 400 = 0Substituting 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. gives14.8806 * h = 400h = 400/14.8806h = 26.8806 (to 4 decimal places)