Question

A 10 meter long rope is to be cut into two pieces and square is to be made using each. The difference in the areas enclosed must be 1 1 divided 4 square metres. How should it be cut?

Answer 1

Step-by-step explanation:

According to question  

x + y = 10 --------------(1)

Area of larger square – area of smaller square = 1 1/4 = 5/4

So x^2 – y^2 = 5/4

(x + y)(x – y) = 5/4

10(x – y) = 5/4

(x – y) = 1/8

So 8x – 8y = 1------------(2)

From 1 and 2 we get

x + y = 10 multiply by 8

8x – 8y = 1

So we get

8x + 8y = 80

8x – 8y =  1

16 x = 81

x = 81/16

putting x = 81/16 in 2 we get

8(81/16) - 8y = 1

81/2 - 8y = 1

81/2 = 1 + 8y

81/2 – 1 = 8y

8y = 79/2

y = 79/2 x 1/8

y = 79/16

It's length should be  81/16 and 79/16 after cutting.