question 20 of 25

what is the length of the diagonal of the square shown below?

a. $\sqrt{11}$
b. 11
c. 11$\sqrt{2}$
d. 121
e. $\sqrt{22}$
f. 11$\sqrt{11}$

Question

question 20 of 25

what is the length of the diagonal of the square shown below?

a. $\sqrt{11}$
b. 11
c. 11$\sqrt{2}$
d. 121
e. $\sqrt{22}$
f. 11$\sqrt{11}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "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" ] } ## Identify the geometric properties of the figure Using the *Special Right Triangles* and *45-45-90 Triangle Theorem* knowledge points $$ \begin{aligned} &\text{Shape: Square with side length } s = 11\ &\text{Diagonal splits the square into two } 45^\circ\text{-}45^\circ\text{-}90^\circ \text{ right triangles} \end{aligned} $$ ## Calculate the diagonal length Using the *Pythagorean Theorem* and *45-45-90 Triangle Theorem* knowledge points $$ \begin{aligned} &d = s\sqrt{2}\ &d = 11\sqrt{2} \end{aligned} $$

(A) $\sqrt{11}$

(B) 11

(C) $11\sqrt{2}$

(D) 121

(E) $\sqrt{22}$

(F) $11\sqrt{11}$

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QUESTION IMAGE

Question

Explanation:

Identify the geometric properties of the figure

Calculate the diagonal length

Answer: