Answer: L = 16 inches , W = 12 inches
Step-by-step explanation:
Area = 192[tex]in^{2}[/tex]
Ratio of length to the width = 4 : 3
This means that L = [tex]\frac{4}{3}[/tex] W
Area of a rectangle = Length x width
Substituting A = 192 and L = [tex]\frac{4}{3}[/tex] W into the formula for calculating area of rectangle , we have
192 = [tex]\frac{4}{3}[/tex] W x W
192 = [tex]\frac{4W^{2} }{y}[/tex]
192 X 3 = [tex]4W^{2}[/tex]
576 = [tex]4W^{2}[/tex]
Divide through by 4
144 = [tex]W^{2}[/tex]
Take the square root of both sides
Therefore :
W = 12 inches
Substitute W = 12 into L = 4/3W , which means
L = 4/3 X 12
L = 16 inches
Therefore :
Length = 16 inches and Width = 12 inches
