Question

question 10 of 27
what is the value of x given that figure adcb is an isosceles trapezoid?
image of trapezoid adcb with diagonals ac and bd, labeled ac = 3x + 15, bd = 7x - 9
a. 6
b. 2.4
c. 4
d. 1.5

Explanation:

Step1: Recall property of isosceles trapezoid

In an isosceles trapezoid, the diagonals are equal in length. So, \( AC = BD \).

Step2: Set up the equation

Given \( AC = 3x + 15 \) and \( BD = 7x - 9 \), we set them equal: \( 3x + 15 = 7x - 9 \).

Step3: Solve for x

Subtract \( 3x \) from both sides: \( 15 = 4x - 9 \).
Add 9 to both sides: \( 24 = 4x \).
Divide both sides by 4: \( x = \frac{24}{4} = 6 \).

Answer:

A. 6