Answer:
x = 6.40
Step-by-step explanation:
Applying the formula for the area of a rectangle A=b*h where b is the base and h is the height, we arrive at an expression,
A = x * (2x - 5) = 50
By expanding the LHS expression and moving (subtracting 50 from both sides) 50 to the left hand side we get a quadratic equation.
2x² - 5x - 50 = 0 which can be solved for x. Note that there will be two roots from this equation.
[tex]x = \frac{5\frac{+}{-}\sqrt{5^{2}- 4*2*(-50) }}{2*2} =\frac{5\frac{+}{-}\sqrt{425}}{2*2} = \frac{5}{4} \frac{+}{-} \frac{\sqrt{25}* \sqrt{17}}{4} =\frac{5}{4} \frac{+}{-} \frac{5}{4}* \sqrt{17}[/tex]
Since only one root is positive we can disregard from the other (negative) root. This is because we cannot have a negative side length.
[tex]\frac{5}{4} + \frac{5}{4}* \sqrt{17} = 1.25 + 1.25*\sqrt{17} \approx 6.40[/tex]
