The height of the mural is 4 meters shorter than the width. Find the height in meters of the mural if the are is 96 square meters.

Answer 1

From the first sentence we can write height = width - 4. We also know that the area of the mural is given by area = width * height because we assume it is a rectangle. We can plug the first equation into the second equation and we get area = width * (width - 4). Because we know area = 96 we can write 96 = width * (width - 4). We can then expand this and put all of the terms on one side to get width ^ 2 - 4 * width - 96 = 0. Factoring this we get (width - 12) * (width + 8) = 0. This gives us that the width either equals 12 meters or -8 meters. Because we cannot have a negative length, we know the width must be 12 meters. Plugging this back into the first equation we get height = 12 - 4 so the height is 8 meters.

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