(Q3)A piece of wire 8m in length is cut into two pieces and each piece is bent into a square. Where should the cut in the wire be made if the sum of the areas of these squares is to be 2m2? [Hint:x + y = 8,(
x
4
)2 + (
y
4
)2 = 2
= (
x
4
)2 + (
8 - x
4
)2 = 2]

let the length of the first piece = x m

Then length of the second piece = 8 - x m

∴Side of the 1 st square =
x
4
m and
side of the second square =
8 - x
4
m

Sum of the areas = 2 m2

(
x
4
)2+(
8 - x
4
)2 = 2

=
x2
16
+
64 + x2 - 16x
16
 = 2

x2 + 64 + x2-16x=

2x2 - 16x + 64 =

2x2 - 16x + = 0

2(x2 - 8x + ) = 0

x2 - 8x + = 0

x2 - x - 4x + = 0

x(x - ) - 4(x-) = 0

(x -)(x - 4) = 0

∴x =

∴The cut should be made at the centre making two equal pieces of length m,m.