A rectangle was constructed using 24 square tiles. If you add the length and width of her rectangle together, you would get 11. What is the length and width of this rectangle?

Factors of 24:

2, 12
3, 8
4, 6

42

To find the length and width of the rectangle, we can use algebraic equations based on the given information.

Let's assume the length of the rectangle is 'x' units and the width is 'y' units.

We are told that a rectangle is constructed using 24 square tiles. Each tile represents 1 unit area. So, the area of the rectangle would be xy.

Therefore, we can write the equation:
xy = 24 -- Equation 1

We are also given that if we add the length and width of the rectangle together, we get 11. Mathematically, this can be expressed as:
x + y = 11 -- Equation 2

Now, we have a system of equations with two unknowns.

We can solve this system of equations using substitution or elimination method. Let's use the substitution method here.

From Equation 2, we can rewrite it as:
x = 11 - y

Substitute this value of 'x' into Equation 1:
(11 - y)y = 24

Now, we can simplify and solve for 'y'.

11y - y^2 = 24

Rearrange the equation:
y^2 - 11y + 24 = 0

Now, we factorize the equation:
(y - 3)(y - 8) = 0

This gives us two possible values for 'y':
y = 3 or y = 8

Substitute these values back into Equation 2 to find the corresponding values of 'x'.

For y = 3:
x + 3 = 11
x = 11 - 3
x = 8

For y = 8:
x + 8 = 11
x = 11 - 8
x = 3

So, we find that the length and width of the rectangle can be either (8, 3) or (3, 8).