Question

Mateo’s old bedroom was a square with integer dimensions. His new bedroom is 3 feet wider and 2 feet longer. The increase in area is 46 ft^2. What were the dimensions of Mateo’s old bedroom?

Answer 1

Let x be the length of Mateo's old bedroom, then its width is also x since it is a square.

The new bedroom's length is x + 2 and its width is x + 3. The area of the new bedroom is (x + 2)(x + 3).

We know that the increase in area is 46 ft^2, so we can write an equation:

(x + 2)(x + 3) - x^2 = 46

Expanding the left side of the equation and simplifying, we get:

x^2 + 5x - 40 = 0

Factoring, we get:

(x + 8)(x - 5) = 0

Since the dimensions of the bedroom must be positive, we can discard the negative solution x = -8. Therefore, the length of Mateo's old bedroom is x = 5 feet, and its dimensions are 5 ft by 5 ft.