Question

Two sides of a triangle are 8 cm and 11cm and its perimeter is 32cm. find the area of the triangle

Answer 1

» Two sides of a triangle are 8 cm and 11cm and its perimeter is 32cm.

a = 8 cm

b = 11 cm

Perimeter of triangle = 32 cm

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• We have to find the area of triangle.

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$\boxed{*\: Perimeter\:of\: triangle\:=\:Sum\:of\: it's\:sides}$

A triangle has three sides but we have given two sides. So, we have to find it's third side.

$\implies$ 32 = a + b + c

$\implies$ 32 = 8 + 11 + c

$\implies$ 32 = 19 + c

$\implies$ c = 32 - 19

$\implies$ c = 13

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$\boxed{* \: Area \: of \: triangle \: = \: \sqrt{s(s - a)(s - b)(s - c)}}$

• s = Semi-perimeter = Perimeter/2

$\implies$ 32/2 = 16

$\implies$ $\sqrt{16(16 \: - \: 8)(16 \: - \: 11)(16 \: - \: 13)}$

$\implies$ $\sqrt{16(8)(5)(3)}$

$\implies$ $\sqrt{8 \: \times \: 2 \: \times \: 8 \: \times \: 5 \: \times \: 3 }$

$\implies$ $8\sqrt{ 2 \: \times \: 5 \: \times \: 3 }$

$\implies$ $8\sqrt{ 30 }$ cm²

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$\huge{\bold{Area\: of\: triangle\: =}}$ $\huge8\sqrt{ 30 } \: {cm}^{2}$

_____________ $\bold{[ANSWER]}$