denesh is creating a triangular flower bed using three pieces of wood. the two shorter pieces of wood have lengths of 7 feet and 24 feet. how long, in feet, should the third piece of wood be for denesh to create a right triangle?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Pythagorean Theorem", "Pythagorean Triples" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem", "Pythagorean Triples" ] } ## Identify the given side lengths and the target unknown $$ \begin{aligned} &a = 7 \ &b = 24 \ &c = \text{hypotenuse (third piece of wood)} \end{aligned} $$ ## Apply the Pythagorean theorem to solve for the hypotenuse $$ \begin{aligned} &a^2 + b^2 = c^2 \ &7^2 + 24^2 = c^2 \ &49 + 576 = c^2 \ &625 = c^2 \ &c = \sqrt{625} \ &c = 25 \end{aligned} $$ Denesh is creating a triangular flower bed using three pieces of wood. The two shorter pieces of wood have lengths of 7 feet and 24 feet. How long, in feet, should the third piece of wood be for Denesh to create a right triangle? 25 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Pythagorean Theorem" ] }

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Explanation:

Identify the given side lengths and the target unknown

Apply the Pythagorean theorem to solve for the hypotenuse

Answer: