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In the given figure angle Q is a right angle, PS:QS = 3: 1, RT: QT = 5: 2 and PU: UR = 1 : 1. If area of triangle QTS is 20 cm, then the area of triangle PQR in cm2 is ________ .
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- 150 cm²
- 260 cm²
- 380 cm²
- 280 cm²
Correct Option: D
Let area of triangle PQR be ‘A’
| = | = | |||
| PQ | 1 + 3 | 4 |
| = | = | |||
| QR | 2 + 5 | 7 |
| Area of ∆le QTS = | × SQ × QT | |
| 2 |
| = | × |  | PQ |  | × | | QR | | |||
| 2 | 4 | 7 |
| = | = | × | × | | × PQ × QR | | |||
| 4 | 7 | 2 |
| = | × Area of ∆le PQR | |
| 14 |
Given
| 20cm² = | × A | |
| 14 |
∴ A = 14 × 20 = 280 cm²
