Maths-
General
Easy

Question

During Van Mahotsav, some children planted trees in a triangular region, two sides of which are 18 m and 10 m and the perimeter is 42 m. Find the area of the planted region.

Hint:

Use Heron’s formula

The correct answer is: 21√11 m2


    Let a = 18 m , b = 10 m and third side = c
    It is given that Perimeter of triangle = 42 m
    a + b + c = 42
    18 + 10 + c = 42
    c = 42 – 28 = 14 m
    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 10 plus 14 over denominator 2 end fraction = 21
    Area of triangle = square root of 21 left parenthesis 21 minus 18 right parenthesis left parenthesis 21 minus 10 right parenthesis left parenthesis 21 minus 14 right parenthesis end root
    square root of left parenthesis 3 right parenthesis left parenthesis 7 right parenthesis left parenthesis 3 right parenthesis left parenthesis 11 right parenthesis left parenthesis 7 right parenthesis end root equals 21 square root of 11 straight m squared

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