The sides of a triangle are 16 cm- 30 cm- 34 cm- Its area is 225 cm2225 -3 cm2225 -2 cm2240 cm2

The correct option is D 240 cm^2 Sides of triangle and 16 cm, 30 cm, 34 cm ∴ s= a+b+c/2= 16+30+34/2= 80/2= 40 ∴ Area = √(s(s a)(s b)(s c)) = √(40(40 16)(40 30 ...

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Standard IX

Mathematics

Area of a Triangle - by Heron's Formula

The sides of ...

Question

The sides of a triangle are $16 c m, 30 c m, 34 c m .$ Its area is

$225 c m^{2}$

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225 $\sqrt{3} c m^{2}$

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225 $\sqrt{2} c m^{2}$

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240 $c m^{2}$

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Solution

The correct option is D: $240 c m^{2}$
Sides of triangle and $a = 16 c m, b = 30 c m, c = 34 c m$
$∴ s = \frac{a + b + c}{2} = \frac{16 + 30 + 34}{2} = \frac{80}{2} = 40$
$∴ A r e a = \sqrt{s (s - a) (s - b) (s - c)}$
$= \sqrt{40 (40 - 16) (40 - 30) (40 - 34)}$
$= \sqrt{40 \times 24 \times 10 \times 6}$
$= \sqrt{2 \times 2 \times 10 - --------- - \times 2 \times 2 \times 6 - -------- - \times 10 \times 6}$
$= \sqrt{2 \times 2 - ---- - \times 10 \times 10 - ------ - \times 2 \times 2 - ---- - \times 6 \times 6 - ---- -}$
$= 2 \times 10 \times 2 \times 6 = 240 c m^{2}$

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