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Easy

Question

The sides of a triangle are 8cm, 15cm and 17cm. find its perimeter and its area. Also find the length of the altitude drawn on the side with length 17cm.

hintHint:


The correct answer is: 7.05 cm


    Let a = 15 cm , b = 8 cm , c = 17 cm
    Perimeter = Sum of all sides =  a + b + c
    = 15 + 8 + 17  = 40 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 = 40 over 2 = 20
    Area of triangle = square root of 20 left parenthesis 20 minus 15 right parenthesis left parenthesis 20 minus 8 right parenthesis left parenthesis 20 minus 17 right parenthesis end root
    square root of 20 left parenthesis 5 right parenthesis left parenthesis 12 right parenthesis left parenthesis 3 right parenthesis end root equals square root of left parenthesis 4 right parenthesis left parenthesis 5 right parenthesis left parenthesis 5 right parenthesis left parenthesis 3 right parenthesis left parenthesis 4 right parenthesis left parenthesis 3 right parenthesis end root
    = (4)(5)(3) = 60 cm2
    Also, Area of triangle = 1 half space cross times b cross times h
    60 = 1 half space cross times 17 cross times h
    h = 120 over 17 ⇒ h = 7.05 cm

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