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Triangles on the Same Base (Or Equal Bases) and Equal Areas Will Lie between the Same Parallels

The semi-peri...

Question

The semi-perimeter of a triangle is 96 cm and its sides are in the ratio of 3 : 4 : 5. The area of the triangle is

1542 c m^{2}

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1536 c m^{2}

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1541 c m^{2}

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1555 c m^{2}

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Solution

The correct option is B
$1536 c m^{2}$
Semi-Perimeter = s

$G i v e n : s = 96 c m Perimeter = 2 s = 192 c m Let the sides be 3x, 4x, and 5x. 3 x + 4 x + 5 x = 192 c m \Rightarrow 12 x = 192 c m \Rightarrow x = 16 S e m i - P e r i m e t e r = \frac{3 x + 4 x + 5 x}{2} = 6 x Using heron's formula, A r e a = \sqrt{s (s - a) (s - b) (s - c)} = \sqrt{6 x (6 x - 3 x) (6 x - 4 x) (6 x - 5 x)} = \sqrt{6 x \times 3 x \times 2 x \times x} = \sqrt{36 x^{4}} = \sqrt{(6 x^{2})^{2}} = 6 x^{2} = 6 \times 16 \times 16 = 1536 c m^{2}$

So, option b is correct.

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Similar questions

The lengths of the sides of a triangle are in the ratio 4 : 5 : 3 and its perimeter is 96 cm. Find its area.

4 : 5 : 3

96

3 : 4 : 5

36 c m

c m^{2}

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