What type of triangle has side lengths of 4, 7, and 9?
Acute, Right, Obtuse, The lengths do not form a triangle.

Solution:

Given the lengths of a triangle 4,7,9

For lengths to form a triangle, the sum of any two sides should be greater than the third side.

• 4+ 7= 11 >9
• 7 + 9 = 16 >4
• 4+ 9 = 13 > 7

Hence, the given lengths form a triangle

Let us assume that the triangle formed by these lengths is a right-angled triangle

So, the bigger length (9) would be the hypotenuse

We have the pythagorean theorem to side² + side² = hypotenuse²

⇒ 4² + 7² = 9²

⇒ 16 + 49 = 65 < 81

The above equation is not true, hence it is not a right-angled triangle

If a, b, c are three sides of a triangle such that a² + b² < c², then the triangle will have an obtuse angle

Hence, it is an obtuse triangle.

What type of triangle has side lengths of 4, 7, and 9?

Summary:

The triangle has side lengths of 4, 7, and 9, then it is an obtuse angle triangle.