A rectangle has perimeter 28 and diagonal 10. What is the area of the rectangle?
Answer and explanation
Correct answer: A. 48
- Step 1: Let length be L and width be W. Perimeter = 2*(L + W) = 28, so L + W = 14.
- Step 2: Diagonal satisfies L^2 + W^2 = 10^2 = 100.
- Step 3: Use identity: (L + W)^2 = L^2 + W^2 + 2LW.
- Step 4: 14^2 = 100 + 2LW, so 196 = 100 + 2LW.
- Step 5: 2LW = 96, so area L*W = 48.
Answer
48.
Why not the others: 40 computes (196 - 116)/2; 52 computes 100 - 48; 44 computes (196 - 108)/2.
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