Question

A wire is bent so as to from four sides of square. A length of 4cm is cut from it and remainder is again bent to form the four sides of a square.If the difference in areas of square is 25cm2 how long was the wire before being cut

Answer 1

Let the total length of wire be x
perimeter of first square + perimeter of second square = length of the wire
perimeter of second square is 4 cm (Given)
Area of square = a^2
perimeter = 4 cm Therefore side of the square (a) = 4/4 = 1 cm
therefore area of second square = (1) ^2
= 1 cm2 _____ (1)

Difference in areas = 25cm2
Therefore,
area of 1st square - area of 2nd square = 25cm2
area of 1st square - 1 = 25
area of 1st square = 25 - 1 = 24cm2
area of 1st square = a2
24 = a2
√24 = a
a = 4√6 cm
perimeter of 1st square = 4a
= 4 × 4√6
= 64√6 cm
total length of wire = perimeter of first square + perimeter of second square
= 64√6 - 4
= 60√6 cm
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