Question

a+b=7, b+c=9, a+c=8, find area by heron's formula

Answer 1

as A+B=7.......(1)

B+C=9........... (2)

A+C=8............(3)

multiple (2) by minus,

we get,

-B-C=-9

(+) A+B=7
__________________

A-C=-2......(4)

from (3)&(4)

A-C=-2

(+) A+C=8
________________

2A=6

A=3 in (1),(3) gives

B=4,C=5

by herons formula,

S=A+B+C/2

=3+4+5/2

=12/2

S=6

Area =√S(S-A)(S-B)(S-C)

= √6(6-3)(6-4)6-5)

= √6(3)(2)(1)

=6 Sq.units.

I hope this helps you.........