Question

If ABCD is an isosceles trapezoid, what is the value of X?DсAC = 7% - 21BD = 5x + 13ABO A. 25O B. 32O c. 17O D. 18O E. 26,5o F. Cannot be determined

Answer 1

A quadrilateral is an isosceles trapeziod if and only if the diagonals are congruent

Since the quadrilateral ABCD is an isosceles trapeziod, then

`|AC|=|BD|`

Recall that

`\begin{gathered} AC=7x-21 \\ BD=5x+13 \end{gathered}`

Then we equate the expression above

`\begin{gathered} 7x-21=5x+13 \\ Collect\text{ like terms } \\ 7x-5x=13+21 \\ Simplify\text{the expression} \\ 2x=34 \\ \text{Divide bothsides by 2 } \\ x=(34)/(2) \end{gathered}`

Therefore the value of x is

`x=17`

Therefore x =17

The right option is C