Mr. jones says that he has 3 daughters, the product of whose ages is 72. furthermore,

the children's ages must be 2, 6 and 6years old.

step-by-step explanation:

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