if (abcd) is an isosceles trapezoid, what is the value of (x)?
(ac = 5x - 25)
(bd = 3x + 11)

a. 26
b. 23
c. 13
d. 18
e. 24.5
f. cannot be determined

Question

if (abcd) is an isosceles trapezoid, what is the value of (x)?
(ac = 5x - 25)
(bd = 3x + 11)

a. 26
b. 23
c. 13
d. 18
e. 24.5
f. cannot be determined

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Isosceles Trapezoid Properties" ], "new_concepts": [], "current_concepts": [ "Isosceles Trapezoid Properties", "Linear Equations" ] } ## Equate the diagonals of the isosceles trapezoid $$ \begin{aligned} AC &= BD \ 5x - 25 &= 3x + 11 \end{aligned} $$ ## Solve for x $$ \begin{aligned} 2x &= 36 \ x &= 18 \end{aligned} $$

A. 26

B. 23

C. 13

D. 18

E. 24.5

F. Cannot be determined

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Isosceles Trapezoid Properties" ] }

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QUESTION IMAGE

Question

Explanation:

Equate the diagonals of the isosceles trapezoid

Solve for x

Answer: