Question

if (a^{2}+b^{2}>c^{2}), what type of triangle is formed? a. acute triangle b. scalene triangle c. isosceles triangle d. right triangle what is the sum of the squares of the legs of a right triangle with sides (a = 5) and (b = 12)? a. 13 b. 169 c. 17 d. 144

Explanation:

Step1: Recall triangle - type rules

In a triangle with side lengths \(a\), \(b\), and \(c\) (where \(c\) is the longest side), if \(a^{2}+b^{2}>c^{2}\), the triangle is acute.

Step2: Recall Pythagorean theorem for right - triangle legs

For a right - triangle with legs \(a\) and \(b\), the sum of the squares of the legs is \(a^{2}+b^{2}\). Given \(a = 5\) and \(b=12\), then \(a^{2}+b^{2}=5^{2}+12^{2}=25 + 144=169\).

Answer:

a. Acute triangle
b. 169