Question

CONNECTING CONCEPTS Find the value of x. Area of trapezoid = 32 X = x + 6 x + 2​

Answer 1

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?