Which type of triangle has side lengths of 4 inches, 7 inches, and 8 inches?

To determine the type of triangle formed by side lengths of 4 inches, 7 inches, and 8 inches, we can apply the triangle inequality theorem and the properties of triangles.

First, check if the triangle inequality theorem holds for these side lengths. The sum of the lengths of any two sides must be greater than the length of the third side:

1. (4 + 7 = 11) which is greater than (8)

2. (4 + 8 = 12) which is greater than (7)

3. (7 + 8 = 15) which is greater than (4)

Since all three conditions are satisfied, these side lengths indeed form a triangle.

Next, to classify the type of triangle, we can apply the Pythagorean theorem to check if it's a right triangle. A triangle is right-angled if the square of the length of the longest side is equal to the sum of the squares of the other two sides.

The longest side here is 8 inches:

• Calculate (4^2 + 7^2):

• (4^2 = 16)

• (7^2 = 49)

• Summing