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

Option A -
`x^2+(x-2)^2 = 100`

Explanation:

Given : 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.

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

Solution :

Let x be the side of the larger square.

We have given that 'one should have a side length two units greater than the other'.

So, the side length of other smaller square is (x-2).

The challenge is to create two squares.

• The number of unit squares included in the larger square is
  `x^(2)`

• The number of unit squares included in the smaller square
  `(x-2)^(2)`

• A group of students is given a 10 by 10 grid to cut into individual unit squares is
  `10^2=100`

This all represent the equation

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

Therefore, Option A is correct.

Answer 2

The correct answer is:

x²+(x-2)² = 100

Explanation:

Let x be the side length of the larger square. Since it is 2 units larger than the smaller square, the side length of the smaller square would be (x-2).

The number of unit squares included in the larger square would be given by the side length squared, or x².

The number of unit squares included in the smaller square would be given by the side length squared, or (x-2)².

Together these would be the number of unit squares in a 10 by 10 square, or 10² = 100.

This gives us the equation

x²+(x-2)² = 100