Question

A group of students is given a 10 by 10 grid to cut into individual unit squares. The challenge is to create two squares using all of the unit squares. Their teacher states that after the two new squares are formed, one should have a side length two units greater than the other.

Which equation represents x, the side length of the greater square?

x2 + (x – 2)2 = 10
x2 + 2x2 = 10
x2 + (x – 2)2 = 100
x2 + 2x2 = 100

Answer 1

Total unit squares = 10×10 = 100. If the larger square has side x and the smaller x−2, their areas add to 100:

x^2 + (x − 2)^2 = 100.

(If you solve it: 2x^2 − 4x − 96 = 0 ⇒ x = 8.)