Question

31. The breadth of a rectangular park is 9 m less than its length. If the perimeter of the field
is 1234 m, find the dimensions of the park.​

Answer 1

Given -

• Perimeter of park 1234 m

• The breadth of a rectangular park is 9 m less than its length.

To Find -

• Dimensions of park

Formula used -

• Perimeter of rectangle

Solution -

In the question, we are provided with two things, first the perimeter of park and second a statement regarding it's dimensions. So, First we will give a name to length of the park, and then we will apply the formula of perimeter of rectangle, then we wil solve the further question.

Let -

The length be termed as x m

Then -

Breadth of park will = x - 9 m

So -

Length = x m

Breadth = x - 9 m

Perimeter = 1234 m

Perimeter of rectangle -

→ 2(l + b)

On applying the formula -

→ Perimeter = 2(l + b)

→ 1234 m = 2[x + x - 9] m

→ 1234 m = 2(2x - 9) m

→ 1234 m = 4x - 18 m

→ 4x = -1234 - 18

[As (-)(-) = +]

→ 4x = 1234 + 18 m

→ 4x = 1252 m

→ x = 1252/2 m

→ x = 131 m

At the end -

Length = x = 131 m

Breadth = x - 9 = 131 - 9 = 304 m

_______________________________

Answer 2

Given :

• The breadth of a rectangular park is 9 m less than its length. If the perimeter of the field is 1234 m

To Find :

• Dimensions of the park

Solutíon :

✬ Here in the question it is given that Breadth of park is 9m less than Length. So, we will let The length be y cm and Breadth be y - 9. Perimeter is given 1234m and we also know that Formuala of Perimeter of rectangle is 2 (Length + Breadth) By putting the values of length and breadth We will get the required Dimensions of the park.

• Let Length be = y

• Breadth be = y - 9

Perimeter of Rectangle = 2(L + B)

⟼ 1234 = 2 (y + y - 9)

⟼ 1234 = 2 (2y -9)

⟼ 1234 = 4y - 18

⟼ 4y = -1234 - 18

⟼ 4y = 1252

⟼ y = 1252/4

⟼ y = 313m

_______________

• Length = x = 313m

• Breadth = x - 9 = 304m

∴ Dimensions of park are 313m, 304m