Question

two consecutive sides of a rectangle are in the ratio 3:2. if its perimeter is 150,then find its area.​

Answer 1

Given :

• Ratio of Dimensions = 3:2
• Perimeter = 150 units

To Find :

• Area = ?

$\\ \qquad{\rule{200pt}{2pt}}$

SolutioN :

$\maltese$ Let the Ratios :

• Length = 3y
• Breadth = 2y

$\maltese$ Formula Used :

• ${\underline{\boxed{\sf{ Perimeter = 2 \bigg( Length + Breadth \bigg) }}}}$

• ${\underline{\boxed{\sf{ Area = Length \times Breadth }}}}$

$\maltese$ Calculating the Value of y :

$\begin{gathered} \qquad \; \longmapsto \; \; \sf { Perimeter = 2 \bigg( Length + Breadth \bigg) } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longmapsto \; \; \sf { 150 = 2 \bigg( 3y + 2y \bigg) } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longmapsto \; \; \sf { 150 = 2 \times 5y } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longmapsto \; \; \sf { 150 = 10y } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longmapsto \; \; \sf { \dfrac{150}{10} = y } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longmapsto \; \; \sf { \cancel\dfrac{150}{10} = y } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longmapsto \; \; {\underline{\boxed{\pmb{\frak{ y = 15 }}}}} \; {\purple{\bigstar}} \\ \\ \\ \end{gathered}$

$\maltese$ Calculating the Dimensions :

• Length = 3y = 3(15) = 45 Units
• Breadth = 2y = 2(15) = 30 Units

$\maltese$ Calculating the Area :

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { Area = Length \times Breadth } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { Area = 45 \times 30 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longmapsto \; \; {\underline{\boxed{\pmb{\frak{ Area = 1350 \; {units}^{2} }}}}} \; {\red{\bigstar}} \\ \\ \\ \end{gathered}$

$\therefore \;$ Area of the Rectangle is 1350 .

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Answer 2

Answer: The area of rectangle is 1350 sq.m

Step-by-step explanation:

Given that the,

Sides of the rectangle are in the ratio of 3:2

Let the length l=2x

and the breadth b=3x

Now, We have to find the area of rectangle

perimeter =2(l+b)=150cm

2(3x+2x)=150

2(5x)=150

10x=150

x=15

Hence, we get the length and breadth of rectangle  are in the ratio 3:2

Therefore, Length l=2x=2*15=30cm

and the breadth b=3x=3*15=45cm

Area of rectangle = length × breadth ( l×b )

A = 30 x 45 = 1350 sq.m

Thus, we get the area of rectangle is 1350 sq.m