Let l be the length of the classroom in feet, and w be the width of the classroom in feet. We know that l + 5 = w and l * w = 84.
We can use these two equations to solve for the length and width of the classroom.
First, we can solve the second equation for l:
l = 84 / w
Substituting this expression for l into the first equation gives us:
84 / w + 5 = w
Expanding the left side of the equation gives us:
84 / w + 5 = w
84 / w = w - 5
84 = w^2 - 5w
w^2 - 5w - 84 = 0
This is a quadratic equation that we can solve using the quadratic formula:
w = (5 + sqrt(5^2 - 4 * 1 * -84)) / 2 * 1
= (5 + sqrt(25 + 336)) / 2
= (5 + sqrt(361)) / 2
= (5 + 19) / 2
= 24 / 2
= 12
Now that we know the value of w, we can substitute it back into the equation l = 84 / w to find the value of l:
l = 84 / 12
= 7
Therefore, the dimensions of the classroom are 7 feet by 12 feet.