We will assume the floor has a rectangular shape.

Let

A = 84 m^2 the area of the floor

w = the width of the floor, w>0

l = the length of the floor, l>0

P = the perimeter of the floor

The area of the floor is:

A = l*w

l*w = 84

The width of the classroom is 5 meters less than the length:

w = l - 5

l = w + 5

Plug l = w + 5 into l*w = 84

(w + 5)*w = 84

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click here to see the solution of the quadratic equation

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w = 7 m

l = w + 5 = 7 + 5

l = 12 m

We plug the values for l and w into the formula for the perimeter of the classroom:

P = 2(l + w)

P = 2(12 + 5)

P = 34 m

The perimeter of the classroom is 34 meters.