A rectangle has length 4 cm longer than its width. It has an area numerically equal to its perimeter. find the width of the rectangle

Question

My math teacher didnt even teach me how to do this

Answer 1

Area of a rectangle is length times width:

A = LW

 

Perimeter is 2L + 2W or 2(L+W)

 

In your problem area equals perimeter:

A = P

 

Length is 4 cm longer than width:

L = W + 4

 

Using the above information:

area = perimeter

LW = 2L + 2W

 

replace L with W+4:

 

(W+4)W = 2(W+4) + 2W

W² + 4W = 2W + 8 + 2W

W² + 4W = 4W + 8

W² = 8

W = √8 = 2√2 cm

 

The width is 2√2 cm