Question

The area of a rectangular land is 3000 sq. meters and perimeter is 220 meters. Out of length and breadth which one is to be increased by what percentage to make it square? Find it.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

• Breadth is to be increased

• Breadth is to be increased by 20% to make the rectangular land square

Given :

The area of a rectangular land is 3000 sq.meters and perimeter is 220 meters

To find :

Out of length and breadth which one is to be increased by what percentage to make it square

Solution :

Step 1 of 3 :

Form the equation to calculate length and breadth of the rectangular land

Let length and breadth of the rectangular land is x meter and y meter respectively

The area of a rectangular land is 3000 sq.meters

∴ xy = 3000 - - - - - - - (1)

The perimeter of the rectangular land is 220 meters

∴ 2(x + y) = 220

⇒ x + y = 110 - - - - - - - (2)

Step 2 of 3 :

Calculate length and breadth of the rectangular land

From Equation 1 and Equation 2 we get

$\displaystyle \sf x(110 - x) = 3000$

$\displaystyle \sf{ \implies } 110x \ - {x}^{2} = 3000$

$\displaystyle \sf{ \implies } {x}^{2} - 110x + 3000 = 0$

$\displaystyle \sf{ \implies } {x}^{2} - (50 + 60)x + 3000 = 0$

$\displaystyle \sf{ \implies } {x}^{2} - 50x - 60x + 3000 = 0$

$\displaystyle \sf{ \implies }x(x - 50) - 60(x - 50) = 0$

$\displaystyle \sf{ \implies }(x - 50)(x - 60) = 0$

$\displaystyle \sf x - 50 = 0 \: \: gives \: \: x = 50$

$\displaystyle \sf x - 60 = 0 \: \: gives \: \: x = 60$

When x = 50 value of y = 60

When x = 60 value of y = 60

Since length > breadth

∴ x = 60 & y = 50

∴ The length and breadth of the rectangular land is 60 meter and 50 meter respectively

Step 3 of 3 :

Calculate out of length and breadth which one is to be increased by what percentage to make it square

The length and breadth of the rectangular land is 60 meter and 50 meter respectively

∴ Breadth is to be increased

Difference between length and breadth of the rectangular land

= 60 meter - 50 meter

= 10 meter

Hence breadth is to be increased by

$\displaystyle \sf = \frac{10}{50} \times 100\%$

$\displaystyle \sf = \frac{1}{5} \times 100\%$

$\displaystyle \sf = 20\%$

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