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guided example 1

the diagonal of the square creates two $45^{\circ}-45^{\circ}-90^{\circ}$ triangles. the legs of the triangles are the sides of the square.

you know the length of the hypotenuse and need to find the length of the legs.

$h = s\sqrt{2}$

$10 = x\sqrt{2}$

write your answer in the form of sqrt(____) with no spaces.

the sides of the square all measure:

Question

apply

guided example 1

the diagonal of the square creates two $45^{\circ}-45^{\circ}-90^{\circ}$ triangles. the legs of the triangles are the sides of the square.

you know the length of the hypotenuse and need to find the length of the legs.

$h = s\sqrt{2}$

$10 = x\sqrt{2}$

write your answer in the form of sqrt(____) with no spaces.

the sides of the square all measure:

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Pythagorean Theorem Application" ], "new_concepts": [ "Special Right Triangles", "Square Properties" ], "current_concepts": [ "Pythagorean Theorem Application", "Special Right Triangles", "Square Properties" ] } ## Set up the relation for a 45-45-90 triangle $$ \begin{aligned} &\text{hypotenuse} = \text{leg} \cdot \sqrt{2} \ &10 = x\sqrt{2} \end{aligned} $$ ## Solve for the leg length x $$ \begin{aligned} &x = \frac{10}{\sqrt{2}} \ &x = \frac{10\sqrt{2}}{2} \ &x = 5\sqrt{2} \end{aligned} $$ ## Convert to the requested form sqrt(...) $$ \begin{aligned} &x = \sqrt{25 \cdot 2} \ &x = \sqrt{50} \end{aligned} $$ The sides of the square all measure sqrt(50) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Special Right Triangles" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the relation for a 45-45-90 triangle

Solve for the leg length x

Convert to the requested form sqrt(...)

Answer: