Question

the length of the base of a triangle is twice its height. if the area of the triangle is 225 square kilometers, find the height. the height is blank

Explanation:

Step1: Recall triangle area formula

The area \( A \) of a triangle is given by \( A = \frac{1}{2} \times \text{base} \times \text{height} \). Here, base is \( 2x \) and height is \( x \), and \( A = 225 \). So substitute into the formula: \( 225=\frac{1}{2}\times(2x)\times x \).

Step2: Simplify the equation

Simplify the right - hand side: \( \frac{1}{2}\times(2x)\times x=x^{2} \). So the equation becomes \( x^{2}=225 \).

Step3: Solve for x

Take the square root of both sides. Since \( x \) represents height (a non - negative quantity), we have \( x = \sqrt{225}=15 \).

Answer:

15 kilometers