Question

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Length and Breadth of a rectangle are in the ratio 2:4 and its perimeter is 100 cm. Find its Area.


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Answer 1

Answer:

Question :

Length and Breadth of a rectangle are in the ratio 2:4 and its perimeter is 100 cm. Find its Area.

$\begin{gathered}\end{gathered}$

Given :

• ➺ Ratio of length and breadth of a rectangle = 2:4
• ➺ Perimeter of rectangle = 100 cm.

$\begin{gathered}\end{gathered}$

To Find :

• ➺ Area of rectangle

$\begin{gathered}\end{gathered}$

Using Formulas :

${\longrightarrow{\small{\underline{\boxed{\sf{\purple{Perimeter_{(Rectangle)}= 2(Length + Breadth)}}}}}}}$

${\longrightarrow{\small{\underline{\boxed{\sf{\purple{Area_{(Rectangle)}= Length \times Breadth}}}}}}}$

$\begin{gathered}\end{gathered}$

Solution :

Here we have given that the ratio between lenght and breadth of rectangle is 2:4. So, let the lenght and breadth be 2x and 4x.

According to the question :

${\implies{\sf{Perimeter_{(Rectangle)}= 2(Length + Breadth)}}}$

${\implies{\sf{100= 2(2x + 4x)}}}$

${\implies{\sf{100= 2(6x)}}}$

${\implies{\sf{100= 2 \times 6x}}}$

${\implies{\sf{100= 12x}}}$

${\implies{\sf{x = \dfrac{100}{12} }}}$

${\implies{\sf{\underline{\underline{\red{x \approx 8.3}}}}}}$

Hence, the value of x is 8.3.

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Now, we know the value of x. So, the length and breadth of rectangle will be :

• ➺ Lenght = 2x = 2×8.3 = 16.6 cm
• ➺ Breadth = 4x = 4×8.3 = 33.3 cm

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Now, finding the area of rectangle by substituting all the given values in the formula :

${\implies{\sf{Area_{(Rectangle)}= Length \times Breadth}}}$

${\implies{\sf{Area_{(Rectangle)}= 16.6\times 33.2}}}$

${\implies{\sf{\underline{\underline\red{Area_{(Rectangle)} \approx \: 551.12 \: {cm}^{2}}}}}}$

Hence, the area of rectangle is 551.12 cm².

$\begin{gathered}\end{gathered}$

Learn More :

$\begin{gathered}\boxed{\begin {minipage}{9cm}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}p\sqrt {4a^2-p^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {minipage}}\end{gathered}$

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Answer 2

Question

Length and Breadth of a rectangle are in the ratio 2 : 4 and its perimeter is 100 cm . Find its Area .

Answer

$= \sf\dfrac{5000}{9} = 555.56 \: {cm}^{2}$

Figure

$\begin{gathered} \sf{ \red{4x \: cm}\:}\huge\boxed{ \begin{array}{cc} \footnotesize{ \pink{\sf \underline{Rectangle}}} \: \: \: \: \: \: \: \\ \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \end{array}} \\ \: \: \: \: \: \sf{ \red{2x \: cm}}\end{gathered}$

Solution

Here , we are given with a rectangle whose length and breadth are in the ratio 2 : 4 respectively. Thus , Let's assume its respective Length = 2x and Breadth = 4x , Also we are provided with a Perimeter = 100 cm

We know that ,

Perimeter of Rectangle = 2(L + B)

Therefore ,

$:↦ \sf100 = 2(2x + 4x)$

$:↦ \sf100 = 2(6x)$

$:↦ \sf100 = 12x$

$:↦ \sf x = \cancel\dfrac{100}{12} \quad = \red{ \dfrac{25}{3}}$

Now , since we get the measure for x we can easily calculate its respective length and breadth

$\sf \: Length = 2x = 2× \dfrac{25}{3} = \red{\dfrac{50}{3} cm}$

$\sf \: Breadth = 4x = 4 \times \dfrac{25}{3} = \red{\dfrac{100}{3}cm }$

Now , what we have to calculate is area of the rectangle

Area of Rectangle = length × Breadth

$\sf Area \: of \: Rectangle = \dfrac{50}{3} \times \dfrac{100}{3}$

$:↦ \sf \: Area \: of \: Rectangle = \dfrac{5000}{9}$

$\rm \: Area \: of \: Rectangle = 555.56 {cm}^{2} \: (approx)$

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