Question

Trapezoid upper A upper B upper C upper D with parallel sides upper A upper B and upper C upper D.
ABCD is a trapezoid with AB¯¯¯¯¯¯¯¯∥CD¯¯¯¯¯¯¯¯ where AD=8x+7 and BC=2x+28 . For what value of x is ABCD an isosceles trapezoid?

(1 point)
Responses

14.5
14.5

3.5
3.5

5.5
5.5

15

Answer 1

In an isosceles trapezoid, the lengths of the non-parallel sides (the legs) are equal. In this case, that means we need to set the lengths of AD and BC equal to each other:

\[
AD = BC
\]

Substituting the expressions for AD and BC:

\[
8x + 7 = 2x + 28
\]

Now, we will solve for \(x\).

1. Subtract \(2x\) from both sides:

\[
8x - 2x + 7 = 28
\]

This simplifies to:

\[
6x + 7 = 28
\]

2. Next, subtract 7 from both sides:

\[
6x = 28 - 7
\]

This simplifies to:

\[
6x = 21
\]

3. Now, divide both sides by 6:

\[
x = \frac{21}{6} = 3.5
\]

Thus, the value of \(x\) for which \(ABCD\) is an isosceles trapezoid is \( \boxed{3.5} \).