As said in the question, P = 2w + 2l
Also from the question, we know that w = 1 + 1/4l because it said that the width of the classroom is 1metre more than 1/4 of its length.
Substitute w =1 + 1/4l into 2w from P = 2w + 2l
So,
P = 2(1 + 1/4l) +2l
Multiply (1 + 1/4l) by 2
So, since P =24
24 = 2 + 2/4l + 2l
Multiply all the units by 4l to remove the denominator which is 4l
So,
24 * 4l =(2 * 4l)+ (2/4l * 4l)+(2l * 4l)
96l = 8l + 2 + 8l²
Collect like terms
96l - 8l = 2 + 8l²
88l = 2 + 8l²
Divide both sides by 88
88l/88 = 2/88 +8l²/88
l = 1/44 + l²/11
Final answer
l = 1/44 + l²/11