The length of an altitude of a triangle is $\frac { 1 } { 2 }$ the length of the side to which it is drawn. If the area of the triangle is 75 square centimeters, find the length of that altitude.
A)5 centimeters
B)4 centimeters
C)10 centimeters
D)3 centimeters
E)8 centimeters

Question

Quizplus · Accepted Answer

The area of a triangle is given by $ \frac{1}{2} \times \text{base} \times \text{height} $. Given that the height (altitude) is $\frac{1}{2}$ the length of the base, let the base be $2x$ and the height be $x$. Thus, the area is $ \frac{1}{2} \times 2x \times x = 75 $ square centimeters. Simplifying gives $x^2 = 75$, so $x = \sqrt{75} = 5$ centimeters.

The Length of an Altitude of a Triangle Is 12\frac { 1 } { 2 }21​

The Length of an Altitude of a Triangle Is $\frac { 1 } { 2 }$