The area of a rectangle is 42 square centimeters. If the perimeter is 34 centimeters, find the length and width of the rectangle.

Question

The area of a rectangle is 42 square centimeters. If the perimeter is 34 centimeters, find the length and width of the rectangle.

Answer 1

Let x = the width

Let y = the length

A = lw

xy = 42   Equation #1

 

P = 2l + 2w

34 = 2x + 2y

34 - 2y = 2x

17 - y = x   Substitute this equation into Eq. #1

 

(17 - y)y = 42

17y - y² = 42

0 = y² - 17y + 42

(y - 3)(y - 14) = 0

y - 3 = 0    or    y - 14 = 0

y = 3         or    y = 14

x = 17 - y         x = 17 - y

x = 17 - 3         x = 17 - 14

x = 14               x = 3

 

length = 14 cm and width = 3 cm

OR

length = 3 cm and width = 14 cm

 

 

 

Answer 2

Let l = length and w=width

 

Perimeter = 2l + 2w = 34  and solve for w

 

w = 17 - l

 

Area = l x w = l(17-l) = 42

 

-L² +17l = 42

 

l² -17l + 42 = 0

 

(l-14)(l-3) = 0

 

l = 14 or 3