1 Answer

Paul Beck · Answer 1 · 2024-02-17T05:29:28+0000

The height (x) of trapezoid is 4.

To find the value of x, you can use the formula for the area of a trapezoid:

$\text{Area} = (1)/(2)h(b_1 + b_2)$

Given that the area is 32, the height (h) is x, and the bases are
$b_1 = x + 6\) and \(b_2 = x + 2$ , you can set up the equation:

$32 = (1)/(2)x(x + 6 + x + 2)$

First, simplify the expression inside the parentheses:

$32 = (1)/(2)x(2x + 8)$

Now, distribute the x:

$32 = x^2 + 4x$

Rearrange the equation into standard quadratic form:

$x^2 + 4x - 32 = 0$

Now, you can factor the quadratic or use the quadratic formula to solve for x. Factoring, we get:

$(x + 8)(x - 4) = 0$

So, the solutions are
$x = -8\) or \(x = 4$ . However, since the height (x) cannot be negative in this context, the only valid solution is
$x = 4$ .

Therefore the height(x) of trapezoid is 4.

The probable question could be

If the area of a trapezoid is 32 and base 1 is x + 6 and base 2 is x+2 and the height = x, how to solve for x?

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