Question

1. find the perimeter. what type of triangle is this? 2.4 in. 4 in. 3.2 in.

Explanation:

Step1: Calculate the perimeter

The perimeter \(P\) of a triangle is the sum of its side lengths. Given side lengths \(a = 2.4\) in, \(b=3.2\) in, and \(c = 4\) in.

$$P=a + b + c$$

$$P=2.4+3.2 + 4$$

$$P = 9.6$$

Step2: Determine the type of triangle

Check the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) (for right - angled triangles).

$$a^{2}=(2.4)^{2}=5.76$$

$$b^{2}=(3.2)^{2}=10.24$$

$$a^{2}+b^{2}=5.76 + 10.24=16$$

$$c^{2}=(4)^{2}=16$$

Since \(a^{2}+b^{2}=c^{2}\), it is a right - angled triangle. Also, all side lengths are different, so it is a scalene triangle. Combining these, it is a scalene right - angled triangle.

Answer:

The perimeter is \(9.6\) inches. This is a scalene right - angled triangle.