Question

A triangle and a parallelogram have the same base and the same area. If the sides of 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

Answer:

12 cm

Step-by-step explanation:

First find the area of triangle by heron's formula side are 26 28 and 30

Area of triangle =336 cm sq.

Now area of parallelogram =base * height

Height = area of parallelogram ÷ base

Height = 336 ÷ 28

Height=12 cm

Answer 2

Given :-

• First side of triangle (a) = 26 cm

• Second side of triangle (b) = 28 cm

• Third side of triangle (c) = 30 cm

To find :-

• Height of parallelogram = ?

Solution :-

$\rm\:s=\dfrac{a+b+c}{2}$

$\rm\longrightarrow\:s=\dfrac{26+28+30}{2}$

$\rm\longrightarrow\:s=\cancel\dfrac{84}{2}$

$\rm\longrightarrow\:s=42\:cm$

Now,

$\green{\bigstar}\:\underbrace{\sf\pink{{Using\:Heron's\:formula}}}$

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

$\rm\:Area=\sqrt{42(42-26)(42-28)(42-30)}$

$\rm\:Area=\sqrt{42\times\:16\times\:14\times\:12}$

$\rm\:Area=\sqrt{7\times\:6\times\:4\times\:4\times\:7\times\:2\times\:6\times\:2}$

$\rm\:Area=7\times\:6\times\:4\times\:2$

$\rm\:Area=336\:c{m}^{2}$

Now,

we know that,

$\rm\:Area\:of\:parallelogram=b\times\:h$

$\rm\:Area\:of\:parallelogram=28\times\:h$

$\rm\therefore\:28\times\:h=336$

$\rm\longrightarrow\:h=\cancel\dfrac{336}{28}$

$\rm\longrightarrow\:h=12\:cm$

Hence,the height of parallelogram will be 12 cm.