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Statistics

Question
CBSEENMA9003246

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

Solution

 a = 18 cm
b = 10 cm Perimeter - 42 cm
⇒ a + b + c = 42
⇒ 18 + 10 + c = 42
⇒ 28 + c = 42
⇒    c = 42 – 28
⇒    c = 14 cm
 space space space space space space space space space space space space space straight s equals 42 over 2 equals 21 space cm
therefore space space space space space Area of the triangle 
       equals 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
equals 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
equals square root of 21 left parenthesis 3 right parenthesis left parenthesis 11 right parenthesis left parenthesis 7 right parenthesis end root
equals space square root of left parenthesis 7 right parenthesis left parenthesis 3 right parenthesis left parenthesis 3 right parenthesis left parenthesis 11 right parenthesis left parenthesis 7 right parenthesis end root
equals space left parenthesis 7 right parenthesis left parenthesis 3 right parenthesis square root of 11 equals 21 square root of 11 space cm squared

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