Avar S.

asked • 04/12/21

The landing for the steps

The landing for the steps leading up to a county courthouse is shaped like a trapezoid. The area of the landing is 1500 square feet. The shorter base is 12 feet longer than the height. The longer base is 4 feet longer than 3 times the height. What is the height? Round to the nearest tenth if necessary.

Michael M.

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04/12/21

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Anthony T. answered • 04/12/21

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Let's go a little further


1500 = (h)[(3h + 4) + (h + 12)] / 2 rearrange equation to get


3000 = 3h2 +4h +h + 12 = 3h2 + 5h +12 substract 3000 from both sides to get


3h2 +5h - 2988 = 0 This is a quadratic equation that can be solved for h using the quadratic formula h = [ -5 ± √ (-52 - 4 x 3 x -29880) ] / 2


Now you should be able to solve it. Discard the negative result.


I got 92.2 m

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Anthony T.

I made a mistake in the quadratic formula calculation. I should have divided by 6 instead of 2. The formula should read h = [ -5 ± √ (-52 - 4 x 3 x -2988) ] / 6 and 29880 should be 2988. The final answer would then be 30.7 m. Sorry for any inconvenience.
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04/13/21

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