(a)One triangle has side lengths 13, 12, and 5.
Compute the sum of the squares of the shorter lengths.
5^2 + 12^2 =
Compute the square of the longest length.
13^2 =
What kind of triangle is it?
Acute triangle
Right triangle
Obtuse triangle
The sum of the squares of the shorter lengths is 5^2 + 12^2 = 25 + 144 = 169.
The square of the longest length is 13^2 = 169.
Therefore, the triangle is a right triangle.
(b)The other triangle has side lengths 11, 6, and 7.
Compute the sum of the squares of the shorter lengths.
6^2 + 7^2 =
Compute the square of the longest length.
11^2 =
What kind of triangle is it?
Acute triangle
Right triangle
Obtuse triangle
The sum of the squares of the shorter lengths is 6^2 + 7^2 = 36 + 49 = 85.
The square of the longest length is 11^2 = 121.
Therefore, the triangle is an acute triangle.
wrong
I apologize for the error.
The sum of the squares of the shorter lengths is 6^2 + 7^2 = 36 + 49 = 85.
The square of the longest length is 11^2 = 121.
Therefore, the triangle is an obtuse triangle.