Question

Q1. A triangle and a parallelogram have the same base and same area. If the

sides of the triangle are 9 cm, 12 cm and 15 cm and the parallelogram

stands on the base 9 cm, find the height of the parallelogram.​

Answer 1

Answer:

Height of the parallelogram is 6 cm

Step-by-step explanation:

The triangle and the parallelogram have same base, i.e., 9 cm.

Three sides of the Δ are given as under:-

Base = 9 cm

Others sides = 12 cm and 15 cm respectively.

Also,

Area of Δ = Area of llgm

which means,

Area of Δ = Base x  Height

Area of Δ = 9 x h

∴ h = 1/9 x ( Area of Δ ) ................ (eq.1)

Now,

Area of Δ = √s(s-a)(s-b)(s-c)

where a,b,c are the sides of the triangle and s is the semi-perimeter of the triangle.

s = (a+b+c)/2

 = (9+12+15)/2

 = 36/2

 = 18 cm

Substitute the value of s,a,b,c in the formula above.

Area of Δ = √18(18-9)(18-12)(18-15)

               = √18(9)(6)(3)

               = √18 x 18 x 9

               = √18² x 3²

               = 18 x 3

               = 54 cm²

Now substitute the value of Area of Δ in eq.1

h = 1/9 x ( Area of Δ )

h = 1/9 x 54

h = 6 cm

∴ Height of the parallelogram is 6 cm.