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# [Solved] Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42cm.

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Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42cm.

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Assume the third side of the triangle to be “x”.

Now, the three sides of the triangle are 18 cm, 10 cm, and “x” cm

It is given that the perimeter of the triangle = 42cm

x = 42 - (18 + 10) cm = 14 cm

∴ The semi perimeter of triangle = 42/2 = 21 cm

Using Heron’s formula,

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

= $$\sqrt{21(21 - 18)(21 - 10)(21 - 14)}cm^2$$

= $$\sqrt{21 \times 3 \times 11 \times 7}m^2$$

= $$21\sqrt{11}cm^2$$

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