What is the length and width of a rectangle with an area of 40square meters and a perimeter of 28 meters

Dimensions are:

Length = 4 ; width = 10

or

Length = 10 ; width = 4

Step-by-step explanation:

let the length = L

let the width = W

we are given the following:

area of rectangle = L × W = 40 m² - - - - - - ( 1 )

perimeter of a rectangle = 2L + 2W = 28 m - - - - - ( 2 )

from equation (2)

2L + 2W = 28

2L = 28 - 2W

dividing both sides by 2

(2L = 28 - 2W) ÷ 2

L = 14 - W  - - - - - - (3)

Next, let us replace the value of L in equation 1 with equation 3

L × W = 40 - - - - (1)

where L = 14 - W

(14 - W) × W = 40

14W - W²  = 40

0 = W² - 14W + 40

solving the quadratic equation

using completing the squares method

W² - 14W + 40

W² [-4W - 10W] + 40 =  0

(W² - 4W) - (10W + 40) = 0

W(W - 4) - 10(W - 4) = 0

W - 10 = 0; ∴ W = 10

or

W - 4 = 0 ;  ∴ W = 4

putting the values of W into equation (3)

L = 14 - W

where W = 10 or 4

L = 14 - 10 = 4

or L = 14 - 4 = 10

∴ Dimensions are:

Length = 4 ; width = 10

or

Length = 10 ; width = 4

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above

step- i d k and i d c : )

you: : 0

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