The perimeter of a rectangle is 86 cm. twice the width exceeds the length by 2cm. write a system and solve to find the dimensions of the rectangle.

There are two equation of the system

(1) The perimeter

2 (w + l) = p

2 (w + l) = 86

(2) The length and the width

2w = l + 2

From the second equation

2w = l + 2

l + 2 = 2w

l = 2w - 2

Subtitute l with 2w - 2 in the first equation to find the width

2 (w + l) = 86

2 (w + 2w - 2) = 86

2 (3w - 2) = 86

6w - 4 = 86

6w = 90

w = 15

Now, find the length by subtituting w with 15

l = 2w - 2

l = 2 (15) - 2

l = 30 - 2

l = 28

The dimension of the rectangle

length = 28 cm

width = 15 cm