jared is constructing a rectangular door for a shed. if the door, shown below, has a width of 42 in. and a diagonal support of 94 in., what is the approximate height?

a. 52 in.
b. 84 in.
c. 103 in.
d. 136 in.

Question

jared is constructing a rectangular door for a shed. if the door, shown below, has a width of 42 in. and a diagonal support of 94 in., what is the approximate height?

a. 52 in.
b. 84 in.
c. 103 in.
d. 136 in.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Pythagorean Theorem" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem", "Geometric Modeling" ] } ## Set up the Pythagorean equation $$ w^2 + h^2 = d^2 $$ ## Substitute the given values and solve for height $$ \begin{aligned} 42^2 + h^2 &= 94^2 \ 1764 + h^2 &= 8836 \ h^2 &= 7072 \ h &= \sqrt{7072} \approx 84.095 \end{aligned} $$ ## Match with the closest option $$ h \approx 84\text{ in.} $$

(A) 52 in.

(B) 84 in.

(C) 103 in.

(D) 136 in.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Pythagorean Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the Pythagorean equation

Substitute the given values and solve for height

Match with the closest option

Answer: