Question

10.The breadth of a rectangular garden is of its length. If its perimeter is 40 m, find its dimensions.

Answer 1

Correct Question:-

The breadth of a rectangular garden is 2/3rd of its length. If the perimeter of the garden is 40 m, find its dimensions.

Answer:-

Let the length of the garden be x m.

Given:

Breadth is 2/3 of length.

→ Breadth of the garden = (2/3) * x = 2x/3 m.

Also,

Perimeter of the garden = 40 m.

We know that,

Perimeter of a rectangle = 2(length + breadth)

Hence,

→ 40 = 2 (x + 2x/3)

→ 40/2 = (3x + 2x) / 3

→ 20 = 5x/3

→ 20 = (5/3) * x

→ 20 * 3/5 = x

→ 12 = x

→ Length (x) = 12 m.

→ Breadth (2x/3) = 2 * 12/3 = 8 m.

Therefore, the dimensions of the garden are 12 m and 8 m.

Answer 2

Correct Question :The breadth of a rectangular garden is 2/3 rd of it's length if it's perimeter is 40 metre.

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Solution :

Let the Length and Breadth be x and 2x/3 respectively.

$\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$\qquad\tiny\bigstar \: \boxed{ \boxed{\sf Perimeter \: of \: rectangular \: garden \: = \: 40 \: m}} \: \bigstar \: \: \: \big\lgroup\bf {Given}\big\rgroup$

$\dag \: \: \sf Perimeter \: of \: rectangle = 2(length + breadth) \: \: \dag$

$\dashrightarrow \: \: \sf 40 \: m \: = 2 \bigg\{x \: + \: \dfrac{2x}{3} \bigg\}$

$\dashrightarrow \: \: \sf 20 \: m \: = \: \dfrac{(3x + 2x)}{3}$

$\dashrightarrow \: \: \sf 20 \: m \: = \: \dfrac{5x}{3}$

$\dashrightarrow \: \: \sf x \: = \: 3 \times \dfrac{20}{5}$

$\dashrightarrow \: \: \sf x\: = \: 3 \: \times \: 4$

$\dashrightarrow \: \: \underline{ \boxed{\sf x \: = \:12 \: m}}$

Therefore,

$\bullet\:\:\textsf{Length of reactangular garden = x = \textbf{12 m}}$

$\bullet\:\:\textsf{Breadth of reactangular garden = 2x/3 = 2(12)/3 = \textbf{8 m}}$