question 7 of 10

given the median $\overline{qr}$ and trapezoid $mnop$, what is the value of $x$?

a. 6
b. 12
c. 8.5
d. 5
e. 7.5
f. cannot be determined

Question

question 7 of 10

given the median $\overline{qr}$ and trapezoid $mnop$, what is the value of $x$?

a. 6
b. 12
c. 8.5
d. 5
e. 7.5
f. cannot be determined

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [], "new_concepts": [ "Trapezoid Midsegment Theorem" ], "current_concepts": [ "Trapezoid Midsegment Theorem", "Linear Equations" ] } ## State the Trapezoid Midsegment Theorem The length of the midsegment (median) of a trapezoid is the average of the lengths of the two parallel bases: $$QR = \frac{MP + NO}{2}$$ ## Substitute the given expressions Substitute $QR = x + 15$, $MP = 9x - 42$, and $NO = 30$ into the formula: $$x + 15 = \frac{(9x - 42) + 30}{2}$$ ## Solve for x Multiply both sides by 2 and simplify: $$ \begin{aligned} 2(x + 15) &= 9x - 12\ 2x + 30 &= 9x - 12\ 42 &= 7x\ x &= 6 \end{aligned} $$

A. 6

B. 12

C. 8.5

D. 5

E. 7.5

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QUESTION IMAGE

Question

Explanation:

State the Trapezoid Midsegment Theorem

Substitute the given expressions

Solve for x

Answer: