Question

3. A triangle and a parallelogram have the same base
and the same area. If the sides of the triangle are
26 cm, 28 cm and 30 cm, and the parallelogram
stands on the base 30 cm, find the height of the
parallelogram.
(CBSE 2012]

Answer 1

Answer:

12cm

Step-by-step explanation:

a = 26 cm, b= 28 cm and c= 30 cm.

Then, calculating the area of the triangle:

So, the semi-perimeter of triangle ABE,

s= a + b + c/2 = 28 + 26 +30/2

= 42 cm.

Therefore, its area will be given by the Heron's formula:

A= √s(s - a)(s - b)(s -c)

= √42(42 – 28)(42 – 26)(42 – 30)

= = √42(14)(16)(12) = √112896 = 336 cm²

Given that the area of the parallelogram is equal to the area of the triangle:

Area of Parallelogram = Area of Triangle

= base x corresponding height = 336 cm²

= 28 x corresponding height = 336 cm²

= height = 336/28 = 12cm

Therefore, the height of the parallelogram is 12cm.

Answer 2

Answer:

$\frac{56}{5} cm$

Step-by-step explanation: