Question

half the perimeter of a rectangular Garden whose length is 12 metre more than its width is 60 metre find the dimensions of the garden​

Answer 1

ATQ,

Half the perimeter of a rectangular Garden whose length is 12 metre more than its width is 60 metre.

We know that,

Perimeter of a rectangle = 2(l + b)

Therefore half of the perimeter = 2(l + b)/2

= Length + Breadth

Now,

Let the breadth (width) of the rectangle be x.

Therefore it's length = x + 12

➡ Length + Breadth = 60m

➡ x + 12 + x = 60m

➡ 2x + 12 = 60m

➡ 2x = 60 - 12

➡ 2x = 48m

➡ x = 48/2

➡ x = 24m

Hence, dimensions of the rectangular garden :-

• Length = x + 12 = 24 + 12 = 36m

• Width = x = 24m

VERIFICATION :-

If half of the perimeter is 60m, then full perimeter = 60 × 2 = 120m

Perimeter of the rectangular garden = 2 (24 + 36)

= 2 × 60

= 120m Hence verified!

Answer 2

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Gívéñ :-

• length of a rectangular garden is 12 metre more than its width
• Perimeter of the rectangular garden = 60m

Tó Fîńd :-

• Length of the rectangle
• Breadth of the rectangle

Sóĺúťíóń :-

Perimeter is the sum of all sides.

Perimeter of a rectangle = 2 ( l + b)

As per the question,

Half the perimeter (1/2) we will substitute this 1/2 in the formula of perimeter of a rectangle.

Rèćťáńgĺé

Perimeter = $\bf\large\frac{1}{2}$ × 2 ( l + b )

Now, 2 will be cancelled,

Perimeter = ( l + b) ----> 1

As per the question,

Let the width of the rectangle be x m

Length of the rectangle = x + 12 m

Substutite these values in equation 1,

60 = x + 12 + x

60 = 2x + 12

60 - 12 = 2x

48 = 2x

x = $\bf\large\frac{48}{2}$

x = 24 m

Breadth = x = 24 m

Substitute value of breadth i.e 24 for value of x in length,

Length = x + 12

Length = 24 + 12 = 36 m

•°• Length of the rectangular garden = 36 m

Breadth of the rectangular garden = 24 m

$\bf{\huge{\underline{\boxed{\tt{\purple{Verification:}}}}}}$

Length = 36 m

Breadth = 24 m

½ Perimeter = 60 m

If we talk about the Perimeter of the rectangular garden, then,

60 = ½ × 2 ( l + b)

60 × 2 = 2 ( l + b)

120 = 2 ( l + b)

Perimeter = 120 m

But since it's mentioned in the question half the perimeter of a rectangular Garden we will consider 60 m and verify our answer.

Perimeter = ½ × 2 ( l + b)

60 = ½ × 2 ( 36 + 24 )

60 = 36 + 24

60 = 60

LHS = RHS

Hence verified.