Question

Area of a Ilgm is 48cm. Its base and altitude are in the ratio of 1: 3. Find the length of its base

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Answer 1

Given :

• Area of Parallelogram is 48 cm² .
• Base and Altitude are in the ratio 1:3 .

To Find :

• Length of its base .

Solution :

$\longmapsto\tt{Let\:Base\:of\:parallelogram\:be=1x}$

$\longmapsto\tt{Let\:Height\:of\:parallelogram\:be=3x}$

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Parallelogram=b\times{h}}$

Putting Values :

$\longmapsto\tt{48=1x\times{3x}}$

$\longmapsto\tt{48={3x}^{2}}$

$\longmapsto\tt{\cancel\dfrac{48}{3}={x}^{2}}$

$\longmapsto\tt{\sqrt{16}=x}$

$\longmapsto\tt\bf{4=x}$

Value of x is 4 .

Therefore :

$\longmapsto\tt{Base\:of\:parallelogram=1(4)}$

$\longmapsto\tt\bf{4\:cm}$

$\longmapsto\tt{Height\:of\:Parallelogram=3(4)}$

$\longmapsto\tt\bf{12\:cm}$

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VERIFICATION :

$\longmapsto\tt{48=1x\times{3x}}$

$\longmapsto\tt{48=1(4)\times{3(4)}}$

$\longmapsto\tt{48=4\times{12}}$

$\longmapsto\tt\bf{48=48}$

HENCE VERIFIED

Answer 2

Step-by-step explanation:

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$\text{\Large\underline{\red{Question:-}}}$

$\Longrightarrow$ ● Area of a Ilgm is 48cm. Its base and altitude are in the ratio of 1: 3. Find the length of its base.

$\text{\Large\underline{\orange{To\ find:-}}}$

● In this question we have to find the length of its base.

$\text{\Large\underline{\green{Given:-}}}$

$\sf We\ have = \begin{cases} \sf\pink{●\ Area\ of\ parallelogram\ is\ 48cm^{2}.} \\ \\ \sf\pink{●\ Base\ and\ Altitude\ are\ in\ the\ ratio\ of\ 1\ :\ 3.} \end{cases}$

$\text{\large\underline{\blue{Formula\ to\ be\ used:-}}}$

$\sf\orange{●\ Area\ of\ parallelogram\ =\ b\ \times\ h\ ●}$

$\text{\Large\underline{\purple{Solution:-}}}$

• The base and altitude are in the ratio of 1 : 3.

So here:-

$\sf{●\ Let\ the\ base\ of\ paralleogram\ =\ 1\ \times\ x\ =\ 1x.}$

$\sf{●\ And\ let\ the\ height\ of\ parallelogram\ =\ 3\ \times\ x\ =\ 3x.}$

By substituting the values:-

$\sf{●\ 48\ =\ 1x\ \times\ 3x}$

$\sf{●\ 48\ =\ 3x^{2}}$

$\sf{●\ \cancel \dfrac{48}{3}\ =\ x^{2}}$

$\sf{●\ \sqrt{16}\ =\ x}$

$\sf{●\ 4\ =\ x}$

$\sf\pink{●\ x\ =\ 4.}$

● The value of x is 4.

Now here:-

$\sf{●\ Base\ of\ parallelogram\ =\ 1x\ =\ 1\ \times\ 4\ =\ 4cm.}$

$\sf{●\ Height\ of\ parallelogram\ =\ 3x\ =\ 3\ \times\ 4\ =\ 12cm.}$

Hence:-

● The length of the base of parallelogram is 4cm.

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