Question

A person is designing a new rectangular garden. Its area must be 344 square feet. List the length and​ width, in​ feet, of all the possible gardens with this area. Use​ whole-number dimensions. Which garden has the least​ perimeter?

Answer 1

(1 x 344) ft

(344 x 1) ft

(2 x 172) ft

(172 x 1) ft

(4 x 86) ft

(86 x 4) ft

(8 x 43) ft

(43 x 8) ft

the garden with the least perimeter is the garden with dimensions 8 x 43

Explanation:

area of a rectangle = length x width

given the area, we can determine the dimensions of the rectangle by calculating the factors of 344. the factors are then multiplied to determine the area

factors of a number are numbers that divide the original number evenly. they are numbers that when used to divide another number, we derive only only numbers

Factors of 344 = 1, 2,2,2,43 and 344

Possible dimensions and their areas

1 x 344 = =344 ft²

2 x 172 = 344 ft²

4 x 86 = 344 ft²

8 x 43 = 344 ft²

Perimeter of a rectangle = 2 x (length + width)

i would use the dimensions i calculated to determine all the possible perimeters

2 x ( 1 + 344) = 690 ft

2 x (2 + 172) = 348 ft

2 x (4 + 86) = 180 ft

2 x (8 + 43) = 102 ft

the garden with the least perimeter is the garden with dimensions 8 x 43