Question

5. Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is
36 m. Find the dimensions of the garden.​

Answer 1

ANSWER:

• Breadth of rectangle = 16 m
• Length of rectangle = 20 m

GIVEN:

• Half the Perimeter of the rectangle = 36 m.
• Length is 4 m more than its width.

TO FIND:

• Length and breadth of the rectangular garden.

SOLUTION:

Let x be the width of the rectangular garden.

Length = (x+4 ) m

Formula:

• Perimeter of rectangle = 2(length+Breadth)

According to the Question:

$\implies \: \dfrac{1}{2} \times 2(x + x + 4) = 36 \\ \\ \implies \: 2x + 4 = 36 \\ \implies \: 2x = 36 - 4 \\ \implies \: 2x = 32 \\ \implies \: x = \dfrac{32}{2} \\ \\ \implies \: x = 16$

Breadth of rectangle = 16 m

Length of rectangle = 16+4

= 20 m

NOTE:

Some important formulas:

Area of Square = (Side)²

Area of rectangle = Length*Breadth

Area of rhombus = Base*Altitude

Area of parallelogram = Base*Altitude

Area of Triangle = (Base*Altitude)/2

Perimeter of Square = 4(side)

Perimeter of rectangle = 2(length+breadth)

Answer 2

Given :-

• The perimeter of rectangular garden whose length is 4m more than its width is 36m.

To Find:-

• Dimensions of the garden.

Solution :-

• According to the Question.

Let the breadth = x

and the length = 4+x

and half perimeter =36 m its mean that here (l+b) is given.

∴ The full perimeter of garden =2 × 36 =72m.

Now,

Perimeter of rectangular garden = 2 (l+b)

➭ 72 = 2× ( 4+x+x)

➭ 72/2 = 4+2x

➭ 36 = 4+2x

➭ 36-4= 2x

➭ 32 = 2x

➭ x = 32/2

➭ x = 16.

∴The breadth of the rectangular garden is 16 m

and the length of rectangular garden is 4+x = 4+16= 20m

∴ The length of the rectangular garden is 20 m.