Question

a triangle and a parallelogram have the same base and the same area if the sides of the triangle are 26cm,28cm ,30cm, and the parallelogram stands on the base 28 cm find the parallelogram

Answer 1

Base of triangle=Base of parallelogram
Area of triangle =Base of parallelogram
a=26cm,b=28cm, c= 30cm
perimeter = 26+28+30=84cm
S(semiperimeter)=1/2× perimeter
=1/2×84=42
Using Heron's formula
Area of triangle =Root s×s-a×s-b×s-c
Root 42(42-26)(42-28)(42-30)
=336cm2(2 means square)
Area of triangle = Area of parallelogram
336= base× height
height = 336/base
height = 12cm

Answer 2

s=a+b+c/2=26+28+30/2=84/2=42
area of triangle=root (s-a)(s-b)(s-c)
=root(42-26)(42-28)(42-30)
=root 16*14*12
=root 4*4*7*2*2*3*2
=4*2root42
=8root 42
area of parallelogram=b*a
8root 42=28*a
a=8root 42/ 28
=24root6/28
=6root6/7