In a trapezoid, the smaller base is 3 more than the height, the larger base is 5 less than 3 times the height, and the area of the trapezoid 45 square centimeters. How do you find, in centimeters, the height of the trapezoid?

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In a trapezoid, the smaller base is 3 more than the height, the larger base is 5 less than 3 times the height, and the area of the trapezoid 45 square centimeters. How do you find, in centimeters, the height of the trapezoid?

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Answer 1 · 2016-11-21T02:12:58

The height is $5$ $5$ cm.

Explanation:

Let the height be $x$ $x$ , the smaller base be $x + 3$ $x + 3$ and the larger base be $3 x - 5$ $3x - 5$ . Recall the area of a trapezoid is given by $A = \frac{(b_{1} + b_{2}) h}{2}$ $A = ((b_1 + b_2)h)/2$ , where $b_{1}$ $b_1$ and $b_{2}$ $b_2$ are the two bases.

$45 = \frac{(x + 3 + 3 x - 5) x}{2}$ $45 = ((x + 3 + 3x - 5)x)/2$

$90 = (4 x - 2) x$ $90 = (4x - 2)x$

$90 = 4 x^{2} - 2 x$ $90 = 4x^2 - 2x$

$0 = 4 x^{2} - 2 x - 90$ $0 = 4x^2 - 2x - 90$

$0 = 2 (2 x^{2} - x - 45)$ $0 = 2(2x^2 - x - 45)$

$0 = 2 x^{2} - 10 x + 9 x - 45$ $0 = 2x^2 - 10x + 9x - 45$

$0 = 2 x (x - 5) + 9 (x - 5)$ $0 = 2x(x -5) + 9(x- 5)$

$0 = (2 x + 9) (x - 5)$ $0 = (2x + 9)(x - 5)$

$x = - \frac{9}{2} and 5$ $x = -9/2 and 5$

A negative answer is impossible, so the height of the trapezoid is $5$ $5$ cm.

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In a trapezoid, the smaller base is 3 more than the height, the larger base is 5 less than 3 times the height, and the area of the trapezoid 45 square centimeters. How do you find, in centimeters, the height of the trapezoid?

1 Answer

Explanation:

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