Respuesta :
Answer:
Width = 3 cm
Length = 5 cm
Step-by-step explanation:
Given :
The length of a rectangle is 13 centimeters less than six times its width.
Its area is 15 square centimeters
To Find: Find the dimensions of the rectangle.
Solution :
Let Width be x .
Since we are given that length of a rectangle is 13 centimeters less than six times its width.
So, length = 6x-13
Now , Formula of area of rectangle = [tex]length \times width[/tex]
We are given area = 15 square cm.
[tex]15=x(6x-13)[/tex]
[tex]15=6x^{2}-13x[/tex]
[tex]6x^{2}-13x-15=0[/tex]
[tex]6x^{2}-18x+5x-15=0[/tex]
[tex]6x(x-3)+5(x-3)=0[/tex]
[tex](6x+5)(x-3)=0[/tex]
[tex](6x+5)(x-3)=0[/tex]
[tex]x=\frac{-5}{6} , x=3[/tex]
Width cannot be negative.
Thus the width is 3 cm
Length = 6x-13 = 6*3-13 =18-13=5 cm
Hence the dimensions of rectangle :
Width = 3 cm
Length = 5 cm
