Find the length of a rectangular lot with a perimeter of 120m if the length is 4m more than the width

It's important to note that the perimeter of a rectangle is equal to the sum of each of its 4 sides... or the sum of 2 times the width + 2 times the height.

let's call the width w and the length L (i'm just using a capital L so it doesn't look like a 1).

so the perimeter = 2w + 2L

we're given that the perimeter is 120m. i'm just going to omit the unit (m) to be sure not to get confused for the time being.

so, 120 = 2w + 2L

we're told that our length (L) is 4m more than the width (w). so L = w + 4.

so, 120 = 2w + 2(w + 4)
we can distribute the 2nd 2 to get 120 = 2w + 2w + 2(4)
120 = 2w + 2w + 8
combine like terms to get 120 = 4w + 8
subtract 8 from both sides to get 112 = 4w
divide both sides by 4 to get 28 = w.

we found that the width is 28, but we're asked for the length. the length is w + 4, and w = 28. so L = 28 + 4 = 32.

so our length is 32m.

First find BE using pythogorean theorem in triangle BEF.
Then draw a line from E to C. Now you have BEC.
Find EC from BEC.
Then you could easily find the required answer ED from triangle CDE.