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The length of the rectangle is 3m less than 5 times its width.

If width of the rectangle = w m, 

Length = 5 x - 3

Now Perimeter of a rectangle = 2 [ length + breadth ]

=> 2 [ ( 5 x - 3 ) + x ]  =  102 m................ (given)

=> 5 x - 3 + x  =  102/2  =  51 m

=> 6 x - 3  =  51

=>  x = 9

Hence  Length of the rectangle =  5 x - 3  =  5 (9) - 3  =  42 m ........ Answer

Width = x = 9 m .................... Answer

length of a rectangle is 3m less than 5 times its width

l = 5w - 3

the perimeter of the rectangle is 102m

2l + 2w = 102

l + w = 51

Substitute for l

(5w - 3) + w = 51

6w - 3 = 51

Add 3 to both sides

6w = 54

Divide both sides by 6

w = 9 <–––– width

l = 5w - 3

l = 5(9) - 3

l = 42 <––––– length

l - 3= 5w; l= 5w + 3

p= 2l + 2w= 10w + 6 + 2w= 12w + 6

102= 12w + 6

12w= 96; w= 8 m, l= 43 m