Maths-
General
Easy

Question

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

hintHint:

Find third side using perimeter

The correct answer is: 69.65 cm2


    Let third side be x
    It is given that Perimeter of triangle = 42 cm
    18 + 10 + x = 42
    x = 42 – 28 = 14
    So, length of third side is 14 cm
    Using Heron’s formula,
    Area of triangle = square root of s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis end root where s = fraction numerator a plus b plus c over denominator 2 end fraction
    s = fraction numerator 18 plus 14 plus 10 over denominator 2 end fraction = 21
    Area of triangle = square root of 21 left parenthesis 21 minus 18 right parenthesis left parenthesis 21 minus 14 right parenthesis left parenthesis 21 minus 10 right parenthesis end root
    square root of 21 left parenthesis 3 right parenthesis left parenthesis 7 right parenthesis left parenthesis 11 right parenthesis end root equals square root of left parenthesis 3 right parenthesis left parenthesis 7 right parenthesis left parenthesis 3 right parenthesis left parenthesis 7 right parenthesis left parenthesis 11 right parenthesis end root
    = 21square root of 11 cm2
    (square root of 11 = 3.31)
    = 69.65 cm2

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