Question

a)The difference between 2 numbers is less than 1. Can the differnce between their squares be greater than 100?
b)Each side of a rectangle became 1ft longer. Can its area become 100 sqfeet greater? Problems a) and b) are related. How?

Answer 1

@KingGeorge

Answer 2

@myininaya

Answer 3

a) Call a and b the 2 numbers. we have:
a - b < 1
a^2 - b^2 > 100
a^2 - b^2 = (a - b)(a + b) > 100 --> (a + b) >100/(a - b).
If the sum of the 2 numbers is > 100, then their squares will be > 100.
b) Call a and b the 2 sides of the rectangle. The area of the rectangle gets 100 sq ft bigger:
(a + 1)(b + 1) > ab + 100
((a + 1)(b + 1) = (ab + a + b + 1) > ab +100
(a + b) + 1 > 100
If the sum of the 2 sides > 99 then the area will > 100.

Answer 4

Good job! Thanx a ton.......now how can I give you a medal. Since I am very new to this site
I don't know how to give a medal yet.