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? A. x^2+(x-2)^2=10 B.x^2+2x^2=10 C. x^2+(x-2)^2=100 C. x^2+2x^2=100

Answer 1

Side of greater square = x units
Side of lesser square = x - 2 units
Area of greater square = x² units²
Area of lesser square = (x - 2)² units²
Total area of 10 x 10 grid = 100 units²
Area of greater square + Area of lesser square = total area
x² + (x - 2)² = 100
The answer is C