let

x = the width

y = the length

P = 76 mm the perimeter

the length is 3 more than 4 times the width of a rectangle:

y = 3 + 4x

the perimeter is 76 mm and we know that the perimeter of rectangle is P = 2(width + length) that is P = 2(x + y)

2(x + y) = 76 divide both sides by 2

x + y = 38

by solving the system of equations:

y = 3 + 4x

x + y = 38

we find:

x = 7 mm

y = 31 mm

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

the dimensions of the rectangle are: the width is 7 mm and the length is 31 mm.