Trapezoid upper A upper B upper C upper D with parallel sides upper A upper B and upper C upper D.

Question

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 \( \boxed{3.5} \).