Question

Find the dimensions of a rectangular piece of land if it's length is 8 metres more than four times it's width and the perimeter of the land is 66 metres.

Answer 1

✬ Length = 28 m ✬

✬ Breadth = 5 m ✬

Step-by-step explanation:

Given:

• Measure of length is 8 metres more than 4 times breadth.
• Perimeter of the rectangular land is 66 metres.

To Find:

• What is the length & breadth of rectangular land ?

Solution: Let the breadth of rectangular land be x m. Therefore,

➸ Length = 8 m more than 4 times of breadth.

➸ Length = (4x + 8)m

As we know that the

★ Perimeter of Rectangle = 2(Length + Breadth)★

Here, A/q

• Perimeter = 66 m

$\implies{\rm }$ 66 = 2 ( Length + Breadth )

$\implies{\rm }$ 66 = 2 ( 4x + 8 + x )

$\implies{\rm }$ 66 = 2 ( 5x + 8 )

$\implies{\rm }$ 66 = 10x + 16

$\implies{\rm }$ 66 – 16 = 10x

$\implies{\rm }$ 50 = 10x

$\implies{\rm }$ 50/10 = x

$\implies{\rm }$ 5 m = x

Hence,

➮ Breadth of land = x = 5 m

➮ Length of land = (4x + 8) = 4(5)+8 = 28 m

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★ Verification ★

➟ 2 ( Length + Breadth ) = 66

➟ 2 ( 28 + 5 ) = 66

➟ 2 (33) = 66

➟ 66 = 66

[ Verified ]

Answer 2

GIVEN:

• Length of rectangular land is 8 metres more than four times it's width
• The perimeter of the land is 66 metres.

TO FIND:

• What is the Length and breadth of the rectangular land ?

SOLUTION:

Let the length of the rectangular land be 'L' m and breadth be 'B' m

➢ Length is 8 metres more than four times it's width

$\bf{\rightharpoonup L = 4B + 8...1) }$

We know that the formula for finding the perimeter of rectangular land is:-

$\bf{\star \: Perimeter = 2(Length + Breadth) \: \star}$

According to question:-

$\sf{\rightharpoonup 66 = 2(4B +8+B)}$

$\sf{\rightharpoonup 66 = 2(5B + 8) }$

$\sf{\rightharpoonup \cancel\dfrac{66}{2} = 5B + 8 }$

$\sf{\rightharpoonup 33 = 5B + 8}$

$\sf{\rightharpoonup 33- 8 = 5B }$

$\sf{\rightharpoonup 25 = 5B }$

$\sf{\rightharpoonup \cancel\dfrac{25}{5} = B}$

$\bf{\star \: Breadth = 5 \: m \: \star}$

Put the value of 'B' in equation 1)

$\sf{\rightharpoonup L = 4 \times 5 + 8 }$

$\sf{\rightharpoonup L = 20 + 8 }$

$\bf{\rightharpoonup L = 28 \: m}$

❝ Hence, the Length and breadth of the rectangular land is 28 m and 5 m respectively. ❞

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