jude is making a door for a door frame with an opening that measures 9 feet by 3 feet. which diagonal length should he use to make a door that fits in the door frame?

10 feet
$\sqrt{90}$ feet
$\sqrt{72}$ feet
12 feet

Question

jude is making a door for a door frame with an opening that measures 9 feet by 3 feet. which diagonal length should he use to make a door that fits in the door frame?

10 feet
$\sqrt{90}$ feet
$\sqrt{72}$ feet
12 feet

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Pythagorean Theorem" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem" ] } ## Identify the dimensions of the right triangle $$ \begin{aligned} a &= 9\text{ feet} \ b &= 3\text{ feet} \end{aligned} $$ ## Apply the Pythagorean theorem to find the diagonal length $$ \begin{aligned} c^2 &= a^2 + b^2 \ c^2 &= 9^2 + 3^2 \ c^2 &= 81 + 9 \ c^2 &= 90 \end{aligned} $$ ## Solve for the diagonal length $$ c = \sqrt{90}\text{ feet} $$

10 feet

$\sqrt{90}$ feet

$\sqrt{72}$ feet

12 feet

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QUESTION IMAGE

Question

Explanation:

Identify the dimensions of the right triangle

Apply the Pythagorean theorem to find the diagonal length

Solve for the diagonal length

Answer: