The perimeter of a triangle is 276 and product of differences of semiperimeter and its respective sides is 496800.Find the area of the triangle ?

Asked by nisha_vini29 | 21st May, 2017, 11:32: PM

Expert Answer:

begin mathsize 14px style Perimeter space of space straight a space triangle equals 276
rightwards double arrow straight a plus straight b plus straight c equals 276
rightwards double arrow Semi minus perimeter equals straight s equals fraction numerator straight a plus straight b plus straight c over denominator 2 end fraction equals 276 over 2 equals 138
Now comma space
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 equals 496800
Thus comma space area space of space 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 138 cross times 496800 end root
equals 8280 space sq. space units end style

Answered by Rashmi Khot | 22nd May, 2017, 09:15: AM