Question

The breath of rectangle gardern is 2/3 of its length .if the perimeter is 40m , find the diamension.​

Answer 1

$\: \: \: \: \huge \star \: \: \: \: \: \: \underline{\red{solution : }} \\ \\ let \: length \: be \: = x \\ \\ \therefore \: breath = \frac{2}{3} \times x \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \pink{perimeter = 40cm}} \\ \\ since \: \\ \\ \: \: \: \star \: perimeter = \: \boxed{ \blue{2(l + b)}} \\ \\ \implies \: 40cm = 2(x + \frac{2}{3} \times x) \\ \\ \implies \: \frac{40cm}{2} = \frac{3x + 2x}{3} \\ \\ \implies \: 20cm = \frac{5x}{3} \\ \\ \implies \: \frac{20cm \times 3}{5} = x \\ \\ \therefore \: x = 4cm \times 3 = \red{ \boxed{ \purple{12cm}}} \\ \\ length = x \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 12m \\ \\ breath = \frac{2}{3} \times x \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{2}{3} \times 12 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times 4 \\ \\ breath \: = \pink{ \boxed{ \green{8cm}}}$

Answer 2

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been a rectangle
• Breadth of rectangle is 2/3 times of its length
• Perimeter of rectangle = 40 m

To Find:

• We need to find the dimensions of rectangle

Solution:

Let the Length of rectangle = x

Breadth of rectangle = $\sf{\dfrac{2x}{3}}$

Since we know that

$\boxed{\sf{\pink{Perimeter \: of \: Rectangle = 2( Length + Breadth )}}}$

________________________________

$\bigstar \: \: \underline{\large\mathfrak\orange{According \: to \: the \: Question:}}$

$\hookrightarrow \sf{ Perimeter = 40 \: m}$

$\hookrightarrow \sf{ 2(Length + Breadth) = 40 \: m}$

$\hookrightarrow \sf{2 \left ( x + \dfrac{2x}{3} \right ) = 40 \: m }$

Taking LCM on LHS

$\hookrightarrow \sf{2 \left ( \dfrac{3x + 2x}{3} \right ) = 40 \: m }$

$\hookrightarrow \sf{2 \times \dfrac{5x}{3} = 40 \: m}$

$\hookrightarrow \sf{ \dfrac{10x}{3} = 40 m }$

Cross Multiplying the terms

$\hookrightarrow \sf{ 10x = 40 \times 3 }$

$\hookrightarrow \sf{10x = 120}$

$\hookrightarrow \sf{ x = \dfrac{120}{10}}$

$\hookrightarrow \sf{x = \cancel{\dfrac{120}{10}}}$

$\hookrightarrow \boxed{\sf{x=12 \: m}}$

________________________________

Hence the dimensions of rectangle are

$\implies \sf{Length = 12 \: m}$

$\implies \sf{Breadth = \dfrac{2 \times 12}{3}}$

$\implies \sf{Breadth = 8 \: m}$

$\boxed{\large\mathfrak\red{Length \: of \: Rectangle = 12 \: m}}$

$\boxed{\large\mathfrak\red{Breadth \: of \: Rectangle = 8 \: m}}$

_______________________________

$\huge\mathfrak\green{Verification:}$

1.) Breadth is 2/3 times of length

$\implies \sf{\dfrac{2}{3} \times Length}$

$\implies \sf{\dfrac{2}{3} \times 12}$

$\implies \sf{8 = Breadth}$

2.) Perimeter of rectangle is 40m

$\implies \sf{Perimeter = 2 (length + breadth)}$

$\implies \sf{Perimeter = 2( 12 + 8 )}$

$\implies \sf{Perimeter = 2 \times 20}$

$\implies \sf{Perimeter = 40 \: m }$

Hence Verified !