The perimeter of a rectangle is 160 metre, and the difference of two sides is…
2019
The perimeter of a rectangle is 160 metre, and the difference of two sides is 48 metre. Find the side of a square whose area is equal to the area of this rectangle.
- A.
32 मीटर / 32 m
- B.
8 मीटर / 8 m
- C.
4 मीटर / 4 m
- D.
16 मीटर / 16 m
- E.
24 मीटर / 24 m
Attempted by 19 students.
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Correct answer: A
Step 1: Let the length and width of the rectangle be l and w. Perimeter = 2(l + w) = 160, so l + w = 80.
Step 2: Given l - w = 48.
Step 3: Solve the system: l + w = 80 and l - w = 48. Adding gives 2l = 128, so l = 64. Then w = 16.
Step 4: Area = l × w = 64 × 16 = 1024 m².
Step 5: Side of square = √1024 = 32 m.
हिन्दी उत्तर:
चरण 1: माना आयत की लंबाई और चौड़ाई क्रमशः l और w है। परिमाप = 2(l + w) = 160, इसलिए l + w = 80।
चरण 2: दिया गया है कि l - w = 48।
चरण 3: निकाय को हल करें: l + w = 80 और l - w = 48। जोड़ने पर 2l = 128, इसलिए l = 64। फिर w = 16।
चरण 4: क्षेत्रफल = l × w = 64 × 16 = 1024 m²।
चरण 5: वर्ग की भुजा = √1024 = 32 m।