Dimensions of a Rectangle

Question

The area of a rectangle is 102 square inches and the perimeter of the rectangle is 46 inches. Find the length and width. 

Answer 1

Area = L x W = 102

Perimeter = 2L + 2W = 46

 

Using the perimeter equation, we can solve for L

2L = 46 - 2W

L = 46/2 - 2W/2

L = 23 - W

 

Plug this value for L into the Area equation

(23 - W)(W) = 102

23W - W² = 102

-W² + 23W = 102

W² - 23W = -102

W² -23W + 102 = 0

 

Solve from here...

 

Answer 2

area is 102 square inches

perimeter is 46 inches

1/2 the perimeter is 23 inches

102=2*3*17=(2*3)*(17)=6*17 and 6+17=23, 1/2 the perimeter

length=17 inches

width=6 inches