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The perimeter of a rectangle and a square are 160 m each. The area of the rectangle is less than that of the square by 100 sq m. The length of the rectangle is
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- 30 m
- 60 m
- 40 m
- 50 m
- 30 m
Correct Option: D
Let the length and breadth of rectangle be x and y m. respectively.
According to the question, 2 (x + y) = 160
| ⇒ x + y = | = 80 m...........(i) | |
| 2 |
Perimeter of square = 160 m
| ∴ Side of square = | = 40 m | |
| 4 |
Now,
Area of rectangle = xy
Area of square = 40 × 40 = 1600 m²
Then,
1600 – xy = 100
⇒ xy = 1600 – 100 = 1500 ..(ii)
Now,
(x – y)² = (x + y)² – 4xy
= (80)² – 4 × 1500
= 6400 – 6000 = 400
⇒ x – y = √400 = 20 ...(iii)
From equations (i) and (iii),
2x = 100
| ⇒ x = | = 50 m | |
| 2 |
