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What is the area of a triangle having perimeter 32cm, one side 11cm and difference of other two sides 5cm?
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- 8√30 cm²
- 5√35 cm²
- 6√30 cm²
- 8√2 cm²
- 8√30 cm²
Correct Option: A
Using Rule 2 and 3,
Let the sides of triangle be a, b and c respectively.
∴ 2s = a + b + c = 32
⇒ 11 + b + c = 32
⇒ b + c = 32 – 11 = 21 .....(i)
and b – c = 5 ......(ii)
By adding equations (i) and (ii)
2b = 26 ⇒ b = 13
⇒ c = 13 – 5 = 8
Now, 2s = 32 ⇒ s = 16 a = 11, b = 13, c = 8
∴ Area of triangle
= √s(s - a)(s - b)(s - c)
= √16(16 - 11)(16 - 13)(16 - 8)
= √16 × 5 × 3 × 8
= 8√30 sq. cm.
