Question

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

Answer 1

The area of triangle is equal to that of parallelogram

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

a = 26 cm

b = 28 cm

c = 30 cm

Hence,

$\tt{\rightarrow s=\dfrac{a+b+c}{2}}$

$\tt{\rightarrow s=\dfrac{26+28+30}{2}}$

s = 42 cm

Now,

${\boxed{\sf\:{Using\;Herons\;Formula :-}}}$

$\tt{\rightarrow\sqrt{s(s-a)(s-b)(s-c)}}$

$\tt{\rightarrow\sqrt{42(42-26)(42-28)(42-30)}}$

$\tt{\rightarrow\sqrt{42\times 16\times 14\times 12}}$

$\tt{\rightarrow\sqrt{7\times 2\times 3\times 2\times 2\times 2\times 2\times 2\times 7\times 2\times 2\times 3}}$

$\tt{\rightarrow\sqrt{2^2\times 2^2\times 2^2\times 2^2\times 3^2\times 7^2}}$

= 2 × 2 × 2 × 2 × 7 cm²

= 16 × 7 cm²

= 336 cm²

Given,

${\boxed{\sf\:{Area\;of\;Parallelogram=Area\;of\; Triangle}}}$

Base × Height = 336 cm²

28cm × Height = 336 cm²

$\tt{\rightarrow Height=\dfrac{336}{28}}$

Height = 12 cm