What’s The Area Of The Triangle?

Can you solve this geometry puzzle?

You don’t know the sides of this triangle. Except you know their relations in terms of x and that they form a right-angled triangle.

Can you use this information to figure out its area?

I recommend you pause the article, grab your pen and paper, and give this a go. When you are ready, keep reading for the solution! ✒️

Solution

We know that all side lengths must be positive.

Based on this inequality, x + 6 must be the hypotenuse of the triangle.

Knowing this we can apply Pythagorean Theorem,

Let’s expand the brackets and rearrange the equation. We should get the following quadratic equation.