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If a and b are the lengths of the sides of a right triangle whose hypotenuse is 10 and whose area is 20, then the value of (a + b)² is
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- 140
- 180
- 120
- 160
- 140
Correct Option: B
Using Rule 1,
BC = a units, AB = b units
AC = √a² + b² = 10
⇒ a² + b² = 100 .......(i)
Area of ∆ABC
= | × base × height | |
2 |
= | ab | |
2 |
∴ | ab = 20 | |
2 |
⇒ ab = 40 square units........(ii)
7there4; (a + b)² = a² + b² + 2ab
= 100 + 2 × 40 = 180 square units