question 5 of 25

in the triangle shown below, what is the approximate value of $x$?

a. 21 units
b. 31.30 units
c. 14 units
d. 24.25 units

Question

question 5 of 25

in the triangle shown below, what is the approximate value of $x$?

a. 21 units
b. 31.30 units
c. 14 units
d. 24.25 units

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" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem", "Right Triangles" ] } ## Identify the given values and formula Using the *Pythagorean Theorem* knowledge point $$ \begin{aligned} &a^2 + b^2 = c^2\ &a = x,\quad b = 14,\quad c = 28 \end{aligned} $$ ## Solve for the unknown side length Using the *Pythagorean Theorem* knowledge point $$ \begin{aligned} &x^2 + 14^2 = 28^2\ &x^2 + 196 = 784\ &x^2 = 588\ &x = \sqrt{588} \approx 24.25 \end{aligned} $$

(A) 21 units

(B) 31.30 units

(C) 14 units

(D) 24.25 units

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Pythagorean Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given values and formula

Solve for the unknown side length

Answer: