Question

The base of a parallelogram is three times its height. If its area is 243cm, find the base and the height of the parallelogram

Answer 1

solutions:-
Given,
base=3×height
area=243cm^2
let height of parallelogram be x cm ,
then, height=3x
area of parallelogram=base×height
243cm^2 =x×3x
243cm^2=3x^2
243/3=x^2
81cm^2=x^2
taking sq. root on both sides,
9=x
height=9cm ,base=9/3=3cm

Answer 2

$\underline{\textbf{Hey Mate Here Is Your Answer }}$

$\underline{\textbf{Given That ..}}$

In A Parallelogram it's Base Is Equal To 3 Times The Height And It's Having an Area Of $\bold{243{cm}^{2}}$.Now We Need To Find It's Base And Height

Now Let's Move For Solution..

$\underline{\textbf{Solution..}}$

Now To Find The measure Of Base And Height Follow The Simple Steps ..

$\underline{\bold{Step-1\: )De f i ne\: All \:Required\: Measures \:With\: Help\: Of \:Variables}}$

So Now Let

$\textbf{Height Of Parallelogram (h) = X }$

Now According To Question Base Is 3 Times The Height ..

Therefore We Have...

$\textbf{Base = 3x}$

$\underline{\textbf{Step-2 )Form An Equation From the Given Information}}$

In Question It's Given That

$\mathbf{Area\: Of \:Parallelogram \:= 243{cm}^{2}}$

So Now We Know That Formula Of Finding Area Of Parallelogram =

$\boxed{\mathbf{Area\: = \:Base\:\times\:Height }}$

Now By Putting Value Of

Base = 3x

And

Height = X

We Have Equation ..

$\boxed{\mathbf{3x \:\times\: x\: =\: 243{cm}^{2}}}$

$\underline{\textbf{Step-3) Solve The Equation}}$

$\mathbf{3x \:\times \:x\: =\: 243{cm}^{2}}$

That Is ...

$\mathbf{3{x}^{2}\: = \:243{cm}^{2}}$

Now Taking 3 To RHS We Have ➡️

$\mathbf{{x}^{2} = \frac{243}{3}}$
That Is ..

$\mathbf{ \:{x}^{2} \:= \:81}$

Now Taking Square To RHS We Have

$\mathbf{x \:=\: \sqrt{81} }$

So We Have ..

$\boxed{\mathbf{x = 9}}$

Therefore Now We Have Value Of

$\underline{\textbf{Step-4) Put The Obtained Value Of X in The Assumed Variable Form}}$

Now We Know That

$\mathbf{Height\: Of \:Parallelogram\: =\: X \longrightarrow\boxed{Height=9cm}}$

$\mathbf{Base \:Of\: Parallelogram \:= 3X \longrightarrow\boxed{Base=3 \:\times\: 9cm \:=\:27cm }}$

$\underline{\textbf{Hence The Required Answer Is ..}}$

$\boxed{\textbf{Base = 27cm And Height = 9cm }}$

$\large{\textbf{Thanks..}}$