(b) The other triangle has side lengths 15,9 , and 12 . Compute the sum of the squares of the shorter lengths. \[ 9^{2}+12^{2}=\square \] Compute the square of the longest length. \( 15^{2}=\square \) What kind of triangle is it? Acute triangle Right triangle Obtuse triangle
Real Tutor Solution
Answer
Solution
Reviewed and approved by the UpStudy tutoring team
Explain 
Simplify this solution Bonus Knowledge
The calculation for the sum of the squares of the shorter lengths goes as follows: \( 9^{2} + 12^{2} = 81 + 144 = 225 \). So, \( 9^{2} + 12^{2} = 225 \). Next up, let's compute the square of the longest length: \( 15^{2} = 225 \). Thus, \( 15^{2} = 225 \). Since \( 9^{2} + 12^{2} = 15^{2} \), this indicates that the triangle is a right triangle. You know what that means? This triangle is just a splendid example of a geometrical phenomenon that follows the Pythagorean theorem! Now, if you'd like to dive deeper into triangular types, you might find it fun to explore the world of triangle classification. Besides right triangles, you'll come across acute triangles (all angles less than 90 degrees) and obtuse triangles (one angle greater than 90 degrees). Each has its own set of properties that makes the world of geometry vibrant and lively!
