The length of a rectangle is 5ft longer than twice the width if the perimeter is 58 ft find the length and width of the rectangle

Define x :

Let the width be x.
Width = x
Length = 2x + 5                // Length is 5ft longer than twice the width


Formula for Perimeter :

Perimeter = 2 (Length + Width)


Find Width :

58 = 2 ( 2x + 5 + x)         // Substitute Length and Width into formula
58 = 2 (3x + 5)                // Combine like terms
58 = 6x + 10                    // Apply distributive property
48 = 6x                            // Take away 10 from both sides
6x = 48                            // Switch sides. Make x the subject
x = 8                                // Divide by 6 on both sides


Find Length and Width :

Width = x = 8 ft
Length = 2x + 5 = 2(8) + 5 = 21 ft


The length is 21 ft and the width is 8 ft.

Length= 5+2x
Width = x

Perimeter = 2(l+w)=58
= 2(5+2x+x)=58
= 2(5+3x)=58
= 10+6x =58
= 6x= 48
X= 8
Width=8
Length= 21