Question

the height of a parallelogram is twice its base. if the area of the parallelogram is 338cm sq. find the base and the height.

pls answer fast​

Answer 1

Answer :-

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Concept\;:-}}}$

Here the concept of Areas of Parallelogram has been used. We see we are given that the Height of Parallelogram is twice its Base. So we can take the base as variable and find their values then.

Let's do it !!

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★ Formula Used :-

$\\\;\boxed{\sf{Area\;of\;Parallelogram\;=\;\bf{Base\;\times\;Height}}}$

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★ Solution :-

Given,

» Height of Parallelogram = 2 × Base

» Area of Parallelogram = 338 cm²

• Let the Base of the Parallelogram be 'x'.

• So the Height of the Parallelogram be '2x'.

(given)

By applying these values in the Area of Parallelogram, we get,

$\\\;\;\;\sf{:\Longrightarrow\;\;Area\;of\;Parallelogram\;=\;\bf{Base\;\times\;Height}}$

$\\\;\;\;\sf{:\Longrightarrow\;\;338\;=\;\bf{x\;\times\;2x}}$

$\\\;\;\;\sf{:\Longrightarrow\;\;x\;\times\;2x\;=\;\bf{338}}$

$\\\;\;\;\sf{:\Longrightarrow\;\;2x^{2}\;=\;\bf{338}}$

$\\\;\;\;\sf{:\Longrightarrow\;\;x^{2}\;=\;\bf{\dfrac{338}{2}}}$

$\\\;\;\;\sf{:\Longrightarrow\;\;x^{2}\;=\;\bf{169}}$

$\\\;\;\;\sf{:\Longrightarrow\;\;x\;=\;\bf{\sqrt{169}}}$

$\\\;\;\;\sf{:\Longrightarrow\;\;x\;=\;\bf{13\;\;cm}}$

Hence, x = 13 cm

Now by applying the value of x in Base and Height, we get

• Base = x = 13 cm

$\\\;\underline{\boxed{\tt{Base\;\;of\;\;Parallelogram\;\;=\;\bf{13\;\;cm}}}}$

• Height = 2x = 2(13) = 26 cm

$\\\;\underline{\boxed{\tt{Height\;\;of\;\;Parallelogram\;\;=\;\bf{26\;\;cm}}}}$

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★ More to know :-

$\\\;\sf{\leadsto\;\;Area\;of\;Triangle\;=\;\dfrac{1}{2}\;\times\;Base\;\times\;Height}$

$\\\;\sf{\leadsto\;\;Area\;of\;Square\;=\;(Side)^{2}}$

$\\\;\sf{\leadsto\;\;Area\;of\;Circle\;=\;\pi r^{2}}$

$\\\;\sf{\leadsto\;\;Area\;of\;Rectangle\;=\;Length\;\times\;Breadth}$

$\\\;\sf{\leadsto\;\;Perimeter\;of\;Square\;=\;4\;\times\;(Side)}$

$\\\;\sf{\leadsto\;\;Perimeter\;of\;Rectangle\;=\;2\;\times\;(Length\;+\;Breadth)}$

$\\\;\sf{\leadsto\;\;Perimeter\;of\;Circle\;=\;2\pi r}$

Answer 2

${\large{\bold{\sf{\underline{Understanding \: the \: question}}}}}$

This question says that there is a parallelogram of area 338 cm² and the base and the height are not given we have to find them. But this question also says that the height of a parallelogram is twice its base. Means the height is double than its base.

${\large{\bold{\sf{\underline{Let's \: see \: and \: solve \: the \: question}}}}}$

$\sf Given \; that \begin{cases} & \sf{Area \: of \: parallelogram = \bf{338 \: cm^{2}}} \\ & \sf{Height \: of \: parallelogram = \bf{2 \times base}} \end{cases}$

$\sf To \; find \begin{cases} & \sf{Height \: of \: parallelogram} \\ & \sf{Base \: of \: parallelogram} \end{cases}$

$\sf Solution \begin{cases} & \sf{Height \: of \: parallelogram = \bf{26 \: cm}} \\ & \sf{Base \: of \: parallelogram = \bf{13 \: cm}} \end{cases}$

$\sf Using \: concept \begin{cases} & \sf{Area \: of \: parallelogram \: formula} \end{cases}$

$\sf Using \; formula \begin{cases} & \sf{Area \: of \: parallelogram = \bf{Base \times Height}} \end{cases}$

$\sf We \; also \; write \; these \; as \begin{cases} & \sf{Height \: as \bf{H}} \\ & \sf{Base \: as \bf{B}} \\ & \sf{Area \: as \bf{A}} \end{cases}$

Assumptions :

• Base is a

• Height is 2a

${\large{\bold{\sf{\underline{\underbrace{Procedure \: of \: question}}}}}}$

☞ To solve this question we have to use the formula of paralloelogram and using this we have to take a site on our assumptions and putting the values according to this. We get the value of our ssumption afterthat using that value of a we have to substitute the values in the assumptions of Base and Height.

${\large{\bold{\sf{\underline{\underbrace{Full \: solution}}}}}}$

Using formula of area of paralloegram we have to put the values and we get the following results :

➝ Area of paralloelogram = Base × Height

➝ 338 cm² = a × 2a

➝ a × 2a = 338

➝ 2a² = 338

➝ a² = 338 / 2

➝ a² = 169

➝ a = √169

➝ a = 13 cm

${\bold{\sf{\boxed{Hence, \: value \: of \: a \: is \: 13 \: cm}}}}$

Now substituting the value of a as 13 in the height and base of the paralloelogram.

➝ Base = a = 13 cm.

➝ Height = 2a = 2(13) = 2 × 13 = 26 cm

${\bold{\sf{\boxed{Hence, \: base \: is \: 13 \: cm}}}}$

${\bold{\sf{\boxed{Hence, \: height \: is \: 26 \: cm}}}}$

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