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Question
Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.
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Solution
Let the third side of the triangle be x.
The perimeter of the given triangle = 42 cm
18 cm + 10 cm + x = 42
x = 14 cm
s = `"Perimeter"/2`
= `42/2 cm`
= 21 cm
By Heron's formula,
Area of a triangle = `sqrt(s(s-a)(s-b)(s-c))`
Area of the given triangle = `(sqrt(21(21-18)(21-10)(21-14)))cm^2`
= `(sqrt(21(3)(11)(7)))cm^2`
= `21sqrt11 cm^2`
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