question 25 of 25

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

a. $4\sqrt{2}$
b. 1
c. 2
d. $\sqrt{8}$
e. 4
f. $8\sqrt{2}$

Question

question 25 of 25

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

a. $4\sqrt{2}$
b. 1
c. 2
d. $\sqrt{8}$
e. 4
f. $8\sqrt{2}$

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": [ "45-45-90 Triangle Theorem", "Pythagorean Theorem" ], "new_concepts": [], "current_concepts": [ "45-45-90 Triangle Theorem", "Pythagorean Theorem", "Properties of Squares" ] } ## Identify the geometric properties Using the *45-45-90 Triangle Theorem* and *Pythagorean Theorem* knowledge points $$ \begin{aligned} &\text{Shape is a square with side length } s.\ &\text{Diagonal divides the square into two } 45^\circ\text{-}45^\circ\text{-}90^\circ \text{ right triangles.}\ &\text{Hypotenuse } d = 8. \end{aligned} $$ ## Calculate the side length s Using the *45-45-90 Triangle Theorem* knowledge point $$ \begin{aligned} &s \cdot \sqrt{2} = 8\ &s = \frac{8}{\sqrt{2}}\ &s = \frac{8\sqrt{2}}{2} = 4\sqrt{2} \end{aligned} $$

(A) $4\sqrt{2}$

(B) 1

(C) 2

(D) $\sqrt{8}$

(E) 4

(F) $8\sqrt{2}$

{ "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

Calculate the side length s

Answer: