Question

One side of a square is increased by 2 cm and the other side is decreased by 2 cm. The perimeter of the resulting rectangle is 64 cm. Find the side of the original square.

Answer 1

Answer

• Original side of square = 16cm.

Given

• One side of a square is increased by 2 cm and the other side is decreased by 2 cm. The perimeter of the resulting rectangle is 64 cm.

To Find

• The original side of the square.

Step By Step Explanation

Given that one side of a square is increased by 2 cm and the other side is decreased by 2 cm. The perimeter of the resulting rectangle is 64 cm.

We need to find the original side of the square.

So let's do it !!

Let us consider, Original side be x.

Then, length = x + 2 and breadth = x - 2

$\red\dag\boxed{\bf{Perimeter_{(Rectangle)} = 2(Length + Breadth)}}$

By substituting the values

$\longmapsto \sf64 = 2(x + 2 + x - 2) \\ \\ \longmapsto \sf64 = 2( x+ x + 2 - 2) \\ \\ \longmapsto \sf64 = 2(2x) \\ \\\longmapsto \sf 64 = 4x \\ \\\longmapsto \sf\cancel\cfrac{64}{4} = x \\ \\ \longmapsto \bf 16cm = x$

Therefore the original side of Square = 16cm.

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Answer 2

$\huge\mathtt\pink{A}\mathtt\red{N}\mathtt\blue{S}\mathtt\green{W}\mathtt\purple{E}\mathtt\green{R}$

Given:-

• one side increased by 2 cm
• other side decreased by 2 cm

To find:-

• orginal side

Solution:-

$\\: \: \: \: \: \: \: \rightarrow \mathtt \purple{let \:original \: side \: be \: x}$

$\\: \: \: \: \: \: \: \rightarrow \mathtt \blue{area \: of \: rectangle = 2(l + b)}$

$\\: \: \: \: \: \: \: \rightarrow \mathtt \red{according \: to \: question}$

$\\: \: \: \: \: \: \: \rightarrow \mathtt\green{64 = 2(x + 2 + x - 2)}$

$\\: \: \: \: \: \: \: \rightarrow \mathtt \green{x = 16}$