Question

find the dimension of the rectangular piece of land if its length is 5 metres more than 4 times its width and the perimeter is 66m​

Answer 1

Step-by-step explanation:

We have,

Let, width=xm

∴3xm

Given, rectangle=84m

2(length+width)=84

2(3x+x)=84

2×4x=84

8x=84

x=

8

84

x= 2

21

x=10.5m

Width of rectangle, x=10.5m

Length of rectangle 3x

=3×10.5m

=31.5m

Hence, this is answer.

Answer 2

Answer:

• Length = 27.4 metres.
• Width = x = 5.6 metres

Explanation:

In a rectangular piece of land,

The length is 5 more than 4 times it's width.

And its perimeter is 66m.

Let's assume,

• Width = ‘x’ metres.

Then, It's length will be = (4x + 5) metres.

Now, perimeter is given by,

⇒ 2(l + w)

Where,

• l(length) = (4x + 5) metres.
• w(width) = x metres.

According to the question,

⇒ 66 = 2(x + 4x + 5)

⇒ 66 = 2(5x + 5)

⇒ 66 = 10x + 10

⇒ 66 - 10 = 10x

⇒ 56 = 10x

⇒ 56/10 = x

⇒ 5.6 = x

Hence, the dimensions are :-

• Length = 4x + 5 = 4(5.6) + 5 = 27.4 metres.
• Width = x = 5.6 metres

_____________________

Quick check :-

⇒ Perimeter of the rectangle = 2(l + w)

⇒ 66 = 2(27.4 + 5.6)

⇒ 66 = 2(33)

⇒ 66 = 66