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Statistics

Question
CBSEENMA9003252

Sides of a triangle are in the ratio 13 : 14 : 15 and its perimeter is 84 cm. Find its area.

Solution

Let the sides of the triangle be 13k, 14k and 15k (in cm). Then,
perimeter = a + b + c
= 13k + 14k + 15k
= 42k cm
According to the questions,
42k = 84
rightwards double arrow space space space space straight k equals 84 over 42 equals 2
∴ Sides are 26 cm, 28 cm and 30 cm.
therefore space space space space space space straight s equals fraction numerator straight a plus straight b plus straight c over denominator 2 end fraction
space space space space space space space space space space space equals space fraction numerator 26 plus 28 plus 30 over denominator 2 end fraction
space space space space space space space space space space space space equals space 42 space cm
therefore space space space space Area space equals space square root of straight s left parenthesis straight s minus straight a right parenthesis left parenthesis straight s minus straight b right parenthesis left parenthesis straight s minus straight c right parenthesis end root
space space space space space space space space space space space space space space equals space square root of 42 left parenthesis 42 minus 26 right parenthesis left parenthesis 42 minus 28 right parenthesis left parenthesis 42 minus 30 right parenthesis end root
space space space space space space space space space space space space space space equals space square root of left parenthesis 42 right parenthesis left parenthesis 16 right parenthesis left parenthesis 14 right parenthesis left parenthesis 12 right parenthesis end root
space space space space space space space space space space space space space space equals space 336 space cm squared

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