Question

Fig. 12.15
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
28 cm, find the height of the parallelogram.​

Answer 1

SOLUTION:-

Given:

•A triangle & a parallelogram have the same base & the same area.

•If the side of the triangle are 26cm, 28cm & 30cm & the parallelogram stands on the base 28cm.

To find:

The height of the parallelogram.

Explanation:

In triangle,

There are three side of the ∆.

• A= 26cm
• B= 28cm
• C= 30cm

Using the formula of the Heron's:

$S = \frac{A + B + C}{2} \\ \\ S = \frac{26cm + 28cm+ 30cm}{2} \\ \\ S = \frac{84cm}{2} \\ \\ S = 42cm$

&

Formula of the area of ∆:

$A= \sqrt{s(s - a)(s - b)(s - c} \\ \\ A = \sqrt{42(42 - 26)(42 - 28)(42 - 30)} \\ \\ A = \sqrt{42(16)(14)(12)} \\ \\ A = \sqrt{(6 \times 7)(16)(2 \times 7)(2 \times 6)} \\ \\ A =( 6 \times 4 \times 7 \times 2) {cm}^{2} \\ \\ A = 336 {cm}^{2}$

Now,

In parallelogram,

We know that, area of the parallelogram;

=) Base × Height

Assume the height of the ||gm be R m.

According to the question:

$= > 28 cm\times R = 336 {cm}^{2} \\ \\ = > R= \frac{336 {cm}^{2} }{28cm} \\ \\ = > R = 12cm$

Thus,

The height of of the ||gm is 12cm.