let

l = the length

w = the width

the perimeter of a rectangle is 84m

2(l + w) = 84 divide both sides by 2

l + w = 84/2

l + w = 42

the length is 2 1/2 times the width

2 1/2 = (2*2 + 1)/2 = 5/2

l = (5/2)w

by solving the system of equations

l + w = 42

l = (5/2)w

we find

l = 30 m

w = 12m

click here to see the step by step solution of the system of equations

the length is 30m and the width is 12m.