Question

find the area of triangle with permeter 22 cm one side is 9 cm and difference of other two sides is 7 cm

Answer 1

let x and y are other 2 sides
given , p=22cm
   one side =9cm
 x-y=7cm      ------------------------------------------eq 1
⇒x+y=p-one side
⇒x+y=22-9=13  ------------------------------------------eq 2
eq 2--------⇒x  +  y  =  13
eq 2--------⇒x  -   y  =   7
                   (-) (+)      (-)
              ------------------------
                       ⇒   2y=6
                       ⇒  y   =3
eq 2⇒x+y=13
        ⇒x+3=13
        ⇒x     =10
ar of Δle=√s(s-a)(s-b)(s-c)
s=22/2=11cm
a=3 b=9 c=10
⇒ar=√11(11-3)(11-9)(11-10)
⇒ar=√11×8×2×1
⇒ar=√11×16
⇒ar=4√11 cm²