Question

If the area of a triangle with base \( x \) is equal to the area of a square with side \( x \), then the altitude of the triangle is:

• A. \( x \)
• B. \( 3x \)
• C. \( 2x \)
• D. \( x/2 \)

Hint:

Equate both areas, cancel the variable where possible, and solve for the unknown height.

Answer 1

The Correct Option is C

Step 1: Area of triangle \[ A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times x \times h \] Step 2: Area of square \[ A_{\text{square}} = x^2 \] Step 3: Equate the areas \[ \frac{1}{2} x h = x^2 \Rightarrow h = \frac{2x^2}{x} = \boxed{2x} \]