Question

A rectangular cutting board has a perimeter of 36 inches and an area of 80 square inches. What are the dimensions of the cutting board?

Answer 1

10 inches x 8 inches.

You can get this by creating two equations.

xy = 80 and 2x + 2y = 36

Then you can solve the first one for either variable. Once you do that you can substitute it into the other equation and solve. You'll get a quadratic equation which will give you both parts of the answer.

Answer 2

The dimension are 10 inches by 8 inches

Explanation:

The rectangular cutting has a perimeter of 36 inches . The area is 80 inches². The dimension can be solved as follows :

perimeter of a rectangle = 2l + 2b

where

l = length

b = breadth

36 = 2l + 2b..............(i)

Area of a rectangle = l × b = lb

80 = lb........................(ii)

l = 80/b

Insert the value of l in equation (i)

36 = 2(80/b) + 2b

36 = 160/b + 2b

36 = (160 + 2b²)/b

cross multiply

36b = 160 + 2b²

2b² - 36b + 160 = 0

b² - 18b + 80 = 0

(b - 8)(b - 10)

b = 8 or b = 10

let us insert b in equation (ii)

80 = lb........................(ii)

80 = l8

l = 80/8

l = 10

or if we insert b =10

80 = lb........................(ii)

80 = 10l

l = 8

The dimension are 10 inches by 8 inches