SAT Math Practice Question #778 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #778

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

A right rectangular prism has a total surface area of \( 144 \) and a space diagonal of length \( \sqrt{52} \). What is the sum of the lengths of all 12 edges of the prism?
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Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
Tactical Insight (Hint 1)

Check for special right triangles (\( 30^\circ-60^\circ-90^\circ \) or \( 45^\circ-45^\circ-90^\circ \)) or the complementary angle identity \( \sin(x) = \cos(90^\circ - x) \).

Elimination Framework (Hint 2)

Elimination Shortcut: Check the extremes or test answer choices starting with C to binary search the correct magnitude.

Masterclass Solution & Distractor Trap Analysis

Step 1: Translate the geometry into algebra. Let the dimensions of the rectangular prism be length \( l \), width \( w \), and height \( h \). 1) The total surface area is \( 144 \). The formula for surface area is: \( 2lw + 2lh + 2wh = 144...

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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