Question

A triangle and a parallelogram have same base and same area if the sides of the triangle are 28cm ,38cm,42cm and the longest side is the common base find the altitude of the parallelogram

Answer 1

firstly find the area of a triangle

by hero 's formula

√s(s-a)(s-b)(s-c)

let.a=42 b=38 c=28

a+b+c=2s

42+38+28 =2s

=54

now

√54(54-42)(54-38)(54-28)

√269568

=519

therefore...area of triangle is 519

now .,

Altitude of parallelogram (h)=Area of triangle / base(a)

=519/42

=12 ....

Altitude of the parallelogram is

12 m

Answer 2

GIVEN:-

• a=28cm,b= 38cm and c=42cm.

• The triangle and parallelogram have a Common base.

TO FIND:-

• The altitude or Height of parallelogram.

FORMULAE USED:-

• ${\boxed{\rm{\sqrt{s(s-a) (s-b) (s-c)}}}}$

Now,

$\implies\rm{S=\dfrac{Perimeter}{2}}$

$\implies\rm{S=\dfrac{\cancel{108}}{\cancel{2}}}$

$\implies\rm{s=54cm}$

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

$\implies\rm{\sqrt{54(54-28)(54-38)(54-42)}}$

$\implies\rm{\sqrt{54\times{26}\times{16}\times{12}}}$

$\implies\rm{\sqrt{269568}}$

$\implies\rm{Area\:of\:triangle=519}$

Atq.

• Longest side is the Common base of triangle and parallelogram.They have same area

$\implies\rm{Area\:of\: parallelogram=Base\times{Height}}$

$\implies\rm{519=42\times{h}}$

$\implies\rm{h=\dfrac{\cancel{19}}{\cancel{42}}}$

$\implies\rm{h=12cm}$

Hence, The height of parallelogram is 12cm.