Question

The base of a parallelogram is thrice its height. If the area is 876cm². Find it's base and height. ​

Answer 1

$\underline{ \underline{ \Large \pmb{\sf { {Given:}} }} }$

• Base = Thrice its height

• Area of the parallelogram = 876cm²

$\underline{ \underline{ \Large \pmb{\sf { {To \: calculate:}} }} }$

• Base and height.

$\underline{ \underline{ \Large \pmb{\sf { {Calculation:}} }} }$

✰ Here, we are given that the base of a parallelogram is thrice its height and the the area is 876cm². So, we'll first assume height as "h", and the base will become "3h" as per the question. Then, we'll form an algebraic equation and by solving that equation we'll find the value of h and then base.

⠀⠀⠀⠀⠀_____________

Let,

• Height be "h".

According to the question,

$\longrightarrow$ Base = 3 × Height

$\longrightarrow$ Base = 3h

As we know that,

$\bigstar \: \boxed{\sf { {Area}_{ (\parallel gm)}= Base \times Height }}$

$\longrightarrow \sf { 876 = 3h \times h }$

$\longrightarrow \sf { 876 = 3 \times {h}^{2} }$

$\longrightarrow \sf { \dfrac{876}{3} = {h}^{2} }$

$\longrightarrow \sf { 292 = {h}^{2} }$

$\longrightarrow \sf { \sqrt{292 }=h}$

$\longrightarrow \boxed{\pmb{ \rm \red { 2 \sqrt{73} \: cm =Height}}}$

Also,

$\longrightarrow \sf { 3h = Base }$

$\longrightarrow \sf { 3 \times 2 \sqrt{73} \: cm= Base }$

$\longrightarrow \boxed{\pmb{ \rm \red { 6 \sqrt{73} \: cm =Base}}}$

Therefore, base of the parallelogram is 6√73 cm and height of the parallelogram is 2√73 cm.

Answer 2

Given : The base of a parallelogram is thrice its height and the area of Parallelogram is 876 cm² .

Exigency To Find : The Base and Height of Parallelogram.

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❍ Let's Consider the Height of Parallelogram be x cm .

Given that ,

• The base of a parallelogram is thrice its height.

Then ,

• Height of Parallelogram is 3x cm .

$\dag\:\:\frak{\underline { As,\:We\:know\:that\::}}$

$\dag\:\:\boxed {\sf{ Area_{(Parallelogram)} = \bigg( b \times h \bigg) }}$

Where ,

• b is the Base of Parallelogram & h is the Height of Parallelogram.

$:\implies \sf{ 876 = x \times 3x }\\\\ :\implies \sf{ 876 = 3x^{2} }\\\\ :\implies \sf{ \cancel {\dfrac{876}{3}}= x^2 }\\\\ :\implies \sf{ 292 = x^{2} }\\\\ :\implies \sf{ \sqrt{292} = x }\\\\ :\implies \bf{2\sqrt {73} cm = x }$

Therefore,

• The Height of Parallelogram is x = $\bf{2\sqrt {73} cm}$
• The Base of Parallelogram is 3x = $3 \times 2\sqrt {73} = \bf{6\sqrt{73}cm}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Height \:of\:Parallelogram \:is\:\bf{2\sqrt {73} cm\: }\:\:\&\:Base\:is\:\bf{6\sqrt{73}cm}}}}$

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