If the length is 7 more than 4 times the width of a rectangle and the perimeter is 74mm, what are the dimensions?

Define x :

Let the width be x
Width = x
Length = 4x + 7


Formula :

Perimeter = 2 (Length + Width)

Perimeter = 74
2(4x + 7 + x) = 74       // sub length and width into the equation
2(5x + 7) = 74             // combine like terms
10x + 14 = 74              // Apply distributive property
10x = 60                      // Take away 14 from both sides
x = 6                            // Divide by 10 on both sides


Find Length and Width :

Width = x = 6mm
Length = 4x + 7 = 4(6) + 7 = 31mm


The length is 31mm and its width 6mm.