fran made a rectangle with 36 square tiles.the sum of the length and width is 15.what are the length and width of her rectangle?

Find the factors of 36.

6 * 6
9 + 4
12 * 3
18 * 2
36 * 1

Which of those combinations add up to 15?

12*3

To find the length and width of Fran's rectangle, we need to set up equations based on the given information.

Let's assume the length of the rectangle is "L" and the width is "W" (both measured in units).

According to the problem, Fran made a rectangle with 36 square tiles. The area of a rectangle is equal to the length multiplied by the width. Therefore, we have the equation:

L * W = 36 ---- (Equation 1)

The problem also states that the sum of the length and width is 15. So, we have another equation:

L + W = 15 ---- (Equation 2)

To solve these simultaneous equations, there are several methods, but let's use the substitution method.

First, isolate one variable in Equation 2 (let's isolate L):

L = 15 - W

Then substitute this value of L into Equation 1:

(15 - W) * W = 36

Expanding this equation, we get:

15W - W^2 = 36

Rearranging this equation, we have:

W^2 - 15W + 36 = 0

Now, we can solve this quadratic equation by factoring or applying the quadratic formula. In this case, let's factor it:

(W - 9)(W - 4) = 0

So, we have two possible values for W: W = 9 and W = 4.

Now, substitute each value of W back into Equation 2 to find the corresponding values of L:

For W = 9:
L + 9 = 15
L = 15 - 9
L = 6

For W = 4:
L + 4 = 15
L = 15 - 4
L = 11

Therefore, Fran's rectangle could have dimensions of either 6 units by 9 units or 11 units by 4 units.