Given a triangle with side lengths $5$, $7$, and $10$, which type of triangle is it?

• A. Obtuse triangle
• B. Equilateral triangle
• C. Acute triangle
• D. Right triangle

Answer: (A)

Verified step by step guidance

1. Identify the side lengths of the triangle: 5, 7, and 10.
2. Recall that to determine the type of triangle by its sides, we can use the Pythagorean theorem and compare the squares of the side lengths.
3. Calculate the squares of the side lengths: \$5^2 = 25\(, \)7^2 = 49\(, and \)10^2 = 100$.
4. Check if the triangle is right-angled by seeing if the sum of the squares of the two smaller sides equals the square of the largest side: \$25 + 49\( compared to \)100$.
5. If the sum of the squares of the two smaller sides is less than the square of the largest side, the triangle is obtuse; if equal, it is right; if greater, it is acute.