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The hypotenuse of a right–angled triangle is 39 cm and the difference of other two sides is 21 cm. Then, the area of the triangle is
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- 270 sq. cm
- 450 sq. cm
- 540 sq. cm
- 180 sq. cm
- 270 sq. cm
Correct Option: A
AC = 39 cm.
BC – AB = 21 cm.
On squaring both sides,
(BC – AB)² = 21²
⇒ BC² + AB² – 2BC.AB = 441
⇒ AC² – 2BC.AB = 441
⇒ 39² – 2BC.AB = 212
⇒ 2.BC.AB = 392 – 212
⇒ 2.BC.AB = (39 + 21) (39 – 21)
⇒ 2 BC . AB = 60 × 18
| ⇒ BC.AB = | ||
| 2 |
= 60 × 9
| ∴ Area of triangle = | BC.AC | |
| 2 |
| ∴ Area of triangle = | × 60 × 9 = 270 sq.cm. | |
| 2 |
