question 3 of 10

what is the length of side $s$ of the square shown below?

a. 3
b. 2
c. $3\sqrt{2}$
d. $\sqrt{6}$
e. $6\sqrt{2}$
f. 6

Question

question 3 of 10

what is the length of side $s$ of the square shown below?

a. 3
b. 2
c. $3\sqrt{2}$
d. $\sqrt{6}$
e. $6\sqrt{2}$
f. 6

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Pythagorean Theorem", "Special Right Triangles", "45-45-90 Triangle Theorem" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem", "Special Right Triangles", "45-45-90 Triangle Theorem", "Properties of Squares" ] } ## Identify the geometric properties of the figure Using the *Special Right Triangles* and *45-45-90 Triangle Theorem* knowledge points $$ \begin{aligned} &\text{The diagonal of length } 6 \text{ divides the square into two congruent right triangles.}\ &\text{Each right triangle has angles of } 45^\circ, 45^\circ, \text{ and } 90^\circ.\ &\text{The legs of the triangle represent the side length } s \text{ of the square.} \end{aligned} $$ ## Apply the side length ratio for a 45-45-90 triangle Using the *45-45-90 Triangle Theorem* knowledge point $$ \begin{aligned} &\text{Hypotenuse} = \text{leg} \times \sqrt{2}\ &6 = s\sqrt{2} \end{aligned} $$ ## Solve for the side length s Using the *Pythagorean Theorem* knowledge point $$ \begin{aligned} &s = \frac{6}{\sqrt{2}}\ &s = \frac{6\sqrt{2}}{2} = 3\sqrt{2} \end{aligned} $$

(A) 3

(B) 2

(C) $3\sqrt{2}$

(D) $\sqrt{6}$

(E) $6\sqrt{2}$

(F) 6

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Special Right Triangles" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the geometric properties of the figure

Apply the side length ratio for a 45-45-90 triangle

Solve for the side length s

Answer: