Answer:
The length of rectangle is 7 cm and width is 2 cm.
Step-by-step explanation:
Given that:
Area of rectangle = 14 square centimeters
The length of a rectangle is 3 centimeters less than five times its width.
Let,
L be the length and W be the width of the rectangle.
L = 5W - 3
Area of rectangle = Length * Width
14 = (5W-3)*W
[tex]14=5W^2-3W\\5W^2-3W-14=0[/tex]
Factorizing the equation;
[tex]5W^2-10W+7W-14=0\\5W(W-2)+7(W-2)=0\\(5W+7)(W-2)=0[/tex]
Either,
5W+7 = 0
5W = -7
W = -7/5
Or,
W-2 = 0
W=2
As width of rectangle cannot be negative, therefore,
Width = 2 centimeters
Length = 5(2) -3 = 10-3 = 7
Hence,
The length of rectangle is 7 cm and width is 2 cm.
