Question

A wire is bent so as to form four side of a square. A length of 4 cm is cut from it and reminder is again bent to form the four sides of a square. If the difference in area of square is
${25}cm^{2}$
how long was the wire before being cut?
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Answer 1

Step-by-step explanation:

Let the length of the wire be x cm

Then the length of side of the square formed =

4

x

After the wire is cut its length is x−4 cm.

And the length of side of the square formed =

4

x−4

Given, difference in area of the squares =25

⇒( 4x ) 2 −( 4x−4 ) 2 =25

On expanding squares and simplifying, we get

16

8x−16

=25

⇒8x−16=16×25=400

⇒8x=416

⇒x=52 cm