Answer:
The width of the rectangle is 5
The length of the rectangle is 13
Explanation:
Let's call x the length of the rectangle and y the width of the rectangle.
The length is 2 less than 3 times the width, so
x = 3y - 2
And the area is 65 square meters. Since the area is length times width, we get:
xy = 65
Now, we can replace the first equation x = 3y - 2 on the second one to get
(3y - 2)y = 65
3y(y) - 2y = 65
3y² - 2y = 65
3y² - 2y - 65 = 0
So, using the quadratic equation, we get that the solutions to 3y² - 2y - 65 = 0 are
[tex]\begin{gathered} y=\frac{-(-2)\pm\sqrt[]{(-2)^2-4(3)(-65)}_{}}{2(3)} \\ y=\frac{2\pm\sqrt[]{784}}{6} \\ y=\frac{2\pm28}{6} \\ \text{Then} \\ y=\frac{2+28}{6}=\frac{30}{6}=5 \\ or \\ y=\frac{2-28}{6}=\frac{-26}{6}=-\frac{13}{3} \end{gathered}[/tex]
The solution is y = 5 because the width can't have a negative length.
Then, replacing y = 5 on the first equation, we get:
x = 3y - 2
x = 3(5) - 2
x = 15 - 2
x = 13
Therefore, the length of the rectangle is 13 meters and the width of the rectangle is 5 meters
