Question

question 5 of 10 if abcd is an isosceles trapezoid, what is the value of x? ac = 7x - 21 bd = 5x + 13 a. 25 b. 32 c. 17 d. 18 e. 26.5 f. cannot be determined

Explanation:

Step1: Recall property of isosceles trapezoid

In an isosceles trapezoid, the diagonals are equal. So, $AC = BD$.

Step2: Set up the equation

Set $7x - 21=5x + 13$.

Step3: Solve for x

Subtract $5x$ from both sides: $7x-5x - 21=5x-5x + 13$, which simplifies to $2x-21 = 13$. Then add 21 to both sides: $2x-21 + 21=13 + 21$, getting $2x=34$. Divide both sides by 2: $x=\frac{34}{2}=17$.

Answer:

C. 17