Rectangle from diagonal and perimeter: The diagonal of a rectangle is 17 cm and its perimeter is 46 cm. Find the area (in sq. cm).
Aptitude
Area
Difficulty: Medium
Choose an option
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A110
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B120
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C130
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D140
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ENone of these
Answer
Correct Answer: 120
Explanation
Introduction / Context:This problem combines Pythagoras with perimeter relations to determine a rectangle’s area from diagonal and perimeter.
Given Data / Assumptions:
- Sides a, b (cm).
- Diagonal d = 17 cm so a^2 + b^2 = 17^2 = 289.
- Perimeter P = 46 cm ⇒ a + b = 23.
Concept / Approach:Use identity (a + b)^2 = a^2 + b^2 + 2ab to find ab, which equals the area for rectangles.
Step-by-Step Solution:
(a + b)^2 = 23^2 = 529.a^2 + b^2 = 289.So 529 = 289 + 2ab ⇒ 2ab = 240 ⇒ ab = 120.Area = a*b = 120 sq. cm.Verification / Alternative check:If a = 8 and b = 15, then diagonal √(64+225)=√289=17 and perimeter 2*(8+15)=46; area 120 checks out.
Why Other Options Are Wrong:110, 130, 140 do not satisfy both the diagonal and perimeter constraints simultaneously.
Common Pitfalls:Trying to solve for individual a and b first; area can be obtained directly from the identity without explicit a, b values.
Final Answer:120