Question

triangle with side lengths 5, 12, 13 (partial text 2) visible on the left)

Explanation:

Step1: Check if it's a right triangle

We can use the Pythagorean theorem \(a^2 + b^2 = c^2\), where \(c\) is the longest side. Here, \(a = 5\), \(b = 12\), \(c = 13\).
\(5^2 + 12^2 = 25 + 144 = 169\), and \(13^2 = 169\). So it's a right triangle with legs 5 and 12.

Step2: Calculate the area

The area of a right triangle is \(\frac{1}{2} \times \text{leg}_1 \times \text{leg}_2\).
So area \(= \frac{1}{2} \times 5 \times 12\)
\(= \frac{60}{2} = 30\)

Answer:

The area of the triangle is 30.