Question

A triangle and a parallelogram have the same base and same area . If the sides of the triangles are 40 cm ,24 cm and 32 cm and parallelogram stands on the base 40 cm . Find the height of the parallelogram .

Answer 1

Answer:

The given sides of the traingle are 13cm, 14cm and 15cm. Let a=13cm, b=14cm and c=15cm.

So, semi-perimeter of the triangle is:

s= (a+b+c)/2 = (13 + 14 + 15)/2 = 21 cm

We know,

The area of a triangle is:

A = [s(s-a)(s-b)(s-c)]^1/2

=[21(21-13)(21-14)(21-15)]^1/2

=[21×8×7×6]^1/2

=[7056]^1/2

=84 cm^2

Now,

The area of the triangle and parallelogram is same and both have same bas i.e. 14 cm.

So,

The area of parallelogram is also:

A=84 cm^2

or, b×h=84 [As area of parallelogram = b×h]

or, 14×h=84

or,h = 84/14

Hence, h = 6cm

Thus, the required height of the parallelogram is 6cm.