Question

If one side of a square is increased by 5m and the other side is reduced by 5m,a rectangle is formed whose perimeter is 40m. Find the side of the original square.​

Answer 1

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Given :-

If one side of the square is increased by 5 meters and the other side is reduced by 5 meters and a rectangle is formed.

• perimeter is 40 meters

Required to find :-

• Measurement of the side of a original square ?

Formula used :-

$\boxed{\text{ \bf perimeter of a rectangle = 2 ( length + breadth)}}$

Solution :-

Given information :-

If one side of the square is increased by 5 meters and the other side is reduced by 5 meters and a rectangle is formed.

we need to find the length of the side of a original square !

[ So, we can conclude that ;

The sides of the square are increased and decreased in length leading to formation of rectangle with length and breadth of different measures ]

Recall the properties of a square

According to which !

• All sides of a square are equal

So,

Let , the length of the side of a square be " x " meters

According to the condition ;

If one side is increased by 5 meters

Let, consider this as the length of the rectangle .

So,

Length of the rectangle = ( x + 5 ) meters

Similarly,

It is also mentioned that

If one side is reduced by 5 meters

Let's consider this as the breadth of the rectangle

So,

Breadth of the rectangle = ( x - 5 ) meters

However,

Perimeter of the rectangle = 40 meters

Now,

Using the formula ,

$\: \boxed{\text{ \bf perimeter of a rectangle = 2 ( length + breadth)}}$

Hence,

According to problem

40 meters = 2 [ ( x + 5 ) m + ( x - 5 ) m ]

40 = 2 [ x + 5 + x - 5 ]

+ 5 & - 5 get cancelled due to opposite signs

40 = 2[ 2x ]

40 = 4x

This implies,

4x = 40

x = 40/4

x = 10

Therefore,

Side of the Square = x = 10 cm