Question

A triangle and a parallelogram have the same base and same area.If the side of the triangle are 13cm, 14cm and 15cm and parallelogram stands on the base 14cm find the height of the parallelogram

Answer 1

Area of∆le=area of parallelogram  a=15,b=14,c=13  Area of ∆=√(s(s-a)(s-b)(s-c)) Where s=(a+b+c)÷2  ie,s=(15+14+13)÷2 =42÷2=21  Area of ∆=√(21×(21-15)(21-14)(21-13))  =√(21×6×7×8) =√7056= 84  Area of ∆= area of parallelogram ,,,,,, Area of parallelogram=base×height,, Base=14, 84=14×h H=84÷14=6

Answer 2

Area of ∆le=area of parallelogram

a=15,b=14,c=13

Area of ∆=√(s(s-a)(s-b)(s-c))

Where s=(a+b+c)÷2

s=(15+14+13)÷2

=42÷2=21

Area of ∆=√(21×(21-15)(21-14)(21-13))  

√(21×6×7×8)

=√7056= 84

Area of ∆= area of parallelogram

Area of parallelogram=base×height

Base=14, 84=14×h

H=84÷14=6