II. Short Answer Questions:
7. The base of a parallelogram is three fourth of its height. If the area is 243sqcm, find the
base and height.
Answers
Answer:
Base 27
Height 9 cm
Step-by-step explanation:
Hey Mate Here Is Your Answer
\underline{\textbf{Given That ..}}
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}}243cm
2
.Now We Need To Find It's Base And Height
Now Let's Move For Solution..
\underline{\textbf{Solution..}}
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}}
Step−1)DefineAllRequiredMeasuresWithHelpOfVariables
So Now Let
\textbf{Height Of Parallelogram (h) = X }Height Of Parallelogram (h) = X
Now According To Question Base Is 3 Times The Height ..
Therefore We Have...
\textbf{Base = 3x}Base = 3x
\underline{\textbf{Step-2 )Form An Equation From the Given Information}}
Step-2 )Form An Equation From the Given Information
In Question It's Given That
\mathbf{Area\: Of \:Parallelogram \:= 243{cm}^{2}}AreaOfParallelogram=243cm
2
So Now We Know That Formula Of Finding Area Of Parallelogram =
\boxed{\mathbf{Area\: = \:Base\:\times\:Height }}
Area=Base×Height
Now By Putting Value Of
Base = 3x
And
Height = X
We Have Equation ..
\boxed{\mathbf{3x \:\times\: x\: =\: 243{cm}^{2}}}
3x×x=243cm
2
\underline{\textbf{Step-3) Solve The Equation}}
Step-3) Solve The Equation
\mathbf{3x \:\times \:x\: =\: 243{cm}^{2}}3x×x=243cm
2
That Is ...
\mathbf{3{x}^{2}\: = \:243{cm}^{2}}3x
2
=243cm
2
Now Taking 3 To RHS We Have ➡️
\mathbf{{x}^{2} = \frac{243}{3}}x
2
=
3
243
That Is ..
\mathbf{ \:{x}^{2} \:= \:81}x
2
=81
Now Taking Square To RHS We Have
\mathbf{x \:=\: \sqrt{81} }x=
81
So We Have ..
\boxed{\mathbf{x = 9}}
x=9
Therefore Now We Have Value Of
\underline{\textbf{Step-4) Put The Obtained Value Of X in The Assumed Variable Form}}
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}}HeightOfParallelogram=X⟶
Height=9cm
\mathbf{Base \:Of\: Parallelogram \:= 3X \longrightarrow\boxed{Base=3 \:\times\: 9cm \:=\:27cm }}BaseOfParallelogram=3X⟶
Base=3×9cm=27cm
\underline{\textbf{Hence The Required Answer Is ..}}
Hence The Required Answer Is ..
\boxed{\textbf{Base = 27cm And Height = 9cm }}
Base = 27cm And Height = 9cm
plz like and follow