Question

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

Answer 1

Given :

• Breadth of the rectangular garden is $\sf\dfrac{2}{3}$ of its length.

• Perimeter = 40 m

To Find :

• Dimensions of the garden

Solution :

Let the length of the garden be x then breadth = $\sf\dfrac{2x}{3}$

We know that,

$\bigstar \: \boxed{ \sf \: Perimeter = 2(length + breadth)}$

$\longrightarrow \sf \: 40 = 2(x + \dfrac{2x}{3} )$

$\longrightarrow \sf \: 40 = 2( \dfrac{3x + 2x}{3} )$

$\longrightarrow \sf \: 40 = 2( \dfrac{5x}{3} )$

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

$\longrightarrow \sf \: 40 = \dfrac{10x}{3}$

$\longrightarrow \sf \: 10x = 40 \times 3$

$\longrightarrow \sf \: 10x =120$

$\longrightarrow \sf \: x = \cancel \dfrac{120}{10}$

$\longrightarrow \sf \red{ x = 12 \: m}$

Hence,

$\dag \: \sf \boxed{ \purple{ \sf \: Length \: of \: the \: field = 12 \: m}}$

$\dag \: \sf \boxed{ \purple{ \sf \: Breadth\: of \: the \: field = \frac{2(12)}{3} = 8 \: m }}$

Verification :

$\bigstar \: \boxed{ \sf \: Perimeter = 2(length + breadth)}$

$\longrightarrow \sf \:40 = 2(12 + 8)$

$\longrightarrow \sf \:40 = 24 + 16$

$\longrightarrow \sf \:40 =40$

Hence, Verified!

Answer 2

$\underline{\bold{\red{Given,}}}$

• The Breadth of  a rectangle is 2/3 of its length.
• Perimeter of Rectangle = 40 m.

$\underline{\bold{\red{To \ Find ,}}}$

• Dimension of Rectangle (Length and Breadth)

Solution :

$\implies$ Suppose the length of Rectangle be a

Therefore, The Breadth of Rectangle be 2a/3.

$\mapsto \underline{\sf{\pink{According \ to \ the \ Question :}}}$

• The Perimeter of Rectangle = 40 m.

Therefore,

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

$\implies \sf{2(a + \dfrac{2a}{3} ) = 40}$

$\implies \sf{\dfrac{3a + 2a}{3} = 40}$

$\implies \sf{2(\dfrac{5a}{3} ) = 40}$

$\implies \sf{\dfrac{10a}{3} = 40}$

$\implies \sf{10a = 40 \times 3}$

$\implies \sf{10a = 120}$

$\implies \sf{ a = \dfrac{120}{10}}$

$\implies \boxed{\sf{a = 12}}$

Therefore, The Dimensions of Rectangle shape Garden :-

$\boxed{\bold{\red{The \ Length \ of \ Rectangle = a = 12 \ m}}}$

$\boxed{\bold{\red{The \ Breadth \ of \ Rectangle = \dfrac{2a}{3} = \dfrac{2(12)}{3} = 8 \ m}}}$

$\rule{200}2$

$\huge{\bf{\underline{\pink{Verification :}}}}$

• First Condition : The Breadth of a rectangle is 2/3 of its length.

Now Check :

$\implies \sf{\dfrac{2a}{3} = 8 \ m}$

$\implies \sf{\dfrac{2(12)}{3} = 8 \ m}$

$\implies \sf{\dfrac{24}{3} = 8 \ m}$

$\implies \boxed{\sf{8 \ m = 8 \ m}}$

Therefore, First Condition Proved.

• Second Condition : The Perimeter of Rectangle is 40 m

Now Check :

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

$\implies \sf{40 = 2(12 + 8)}$

$\implies \sf{40 = 2(20)}$

$\implies \boxed{\sf{40 \ m = 40 \ m}}$

Therefore, Second Condition Also Proved.