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?\\(x^2+(x - 2)^2 = 100\\)\\(x^2 + 2x^2 = 100\\)\\(x^2 + 2x^2 = 10\\)\\(x^2+(x - 2)^2 = 10\\)

Explanation:

Step1: Calculate total area

The total area of the 10x10 grid is $10 \times 10 = 100$.

Step2: Define side lengths

Let $x$ = side length of the larger square. The smaller square has side length $x-2$.

Step3: Set up area equation

The sum of the areas of the two squares equals the total grid area: $x^2 + (x-2)^2 = 100$.

Answer:

$x^2 + (x - 2)^2 = 100$