Question

a triangle and a parallel gram have the same Base and the same area if the sides of triangle are 26cm, 28 cm, and 30 cm. find the parallelogram stands on the base 28cm .find the height of the parallelogram. ....​

Answer 1

To Find:-

• Find the height of parallelogram.

Given:-

• A triangle and a parallel gram have the same Base and the same area if the sides of triangle are 26cm, 28 cm, and 30 cm.

Solution:-

$\tt\implies \: 2s = 26 + 28 + 30$

$\tt\implies \: 2s = 84$

$\tt\implies \: s = \dfrac {84} {2}$

$\tt\implies \: s = 42cm$

Using Herons formula

$\tt\implies \: Area = \sqrt{s(s - a)(s - b)(s - c)}$

$\tt\implies \: area = \sqrt{42(42 - 26)(42 - 28)(42 - 30)}$

$\tt\implies \: area = \sqrt{42 \times 16 \times 14 \times 12}$

$\tt\implies \: Area = \sqrt{112896}$

$\tt\implies \: Area = 336 {cm}^{2}$

According to Question:-

Area of traingle = Area of parallelogram

$\tt\implies \: 336 = h \times 28$

$\tt\implies \: 28h = 336$

$\tt\implies \: h = \dfrac {336} {28}$

$\tt\implies \: h = 13cm$

Answer 2

Perimeter of Triangle

2S = 26+28+30 = 84

⇒S = 42cm

(Heron's formula)

Area s(s−a)(s−b)(s−c) 

Area = 42(42−26)(42−28)(42−30) = 42×16×14×12

$area \: = 336cm {}^{2}$

Area of parallelogram = Area of triangle

⇒ h × 28=336

⇒h = 12cm

Height of parallelogram =12cm