Answer:
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
