-
The sum of the length and breadth of a rectangle is 6 cm. A square is constructed such that one of its sides is equal to a diagonal of the rectangle. If the ratio of areas of the square and rectangle is 5 : 2, the area of the square in cm² is
-
- 20
- 10
- 4√5
- 10√2
- 20
Correct Option: A
Let, AB = a cm.
BC = b cm.
According to the question, a + b = 6 ..... (i)
and diagonal of rectangle
= √a² + b² = side of square
| ∴ | |
| Area of rectangle |
| = | |
| ab |
| ⇒ | = | ||
| 2 | ab |
| ⇒ | = | ||
| 4 | 2ab |
| ⇒ | = | ||
| 5 - 4 | a² + b² - 2ab |
[By componendo and dividendo]
| ⇒ | = | ||
| 1 | (a - b)² |
| ⇒ | = | ||
| 1 | (a - b)² |
| ⇒ (a - b)² = | = 4 | |
| 9 |
⇒ a – b = 2 ..... (ii)
∴ Area of square = a² + b²
| = | [(a + b)² + (a - b)²] | |
| 2 |
| = | (36 + 4) | |
| 2 |
| = | × 40 = 20 sq. cm. | |
| 2 |
