Question

determine whether a triangle with the given side lengths is a right triangle.
side lengths right triangle not a right triangle not enough information
(a) 10, 26, 28
(b) 10, 11, 15
(c) 6, 8, 10
(d) 14, 48, 50

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side.

Step2: Check (a) 10, 26, 28

\(10^{2}+26^{2}=100 + 676=776\), \(28^{2}=784\). Since \(10^{2}+26^{2}
eq28^{2}\), it's not a right - triangle.

Step3: Check (b) 10, 11, 15

\(10^{2}+11^{2}=100 + 121 = 221\), \(15^{2}=225\). Since \(10^{2}+11^{2}
eq15^{2}\), it's not a right - triangle.

Step4: Check (c) 6, 8, 10

\(6^{2}+8^{2}=36 + 64 = 100\), \(10^{2}=100\). Since \(6^{2}+8^{2}=10^{2}\), it's a right - triangle.

Step5: Check (d) 14, 48, 50

\(14^{2}+48^{2}=196+2304 = 2500\), \(50^{2}=2500\). Since \(14^{2}+48^{2}=50^{2}\), it's a right - triangle.

Answer:

(a) Not a right triangle
(b) Not a right triangle
(c) Right triangle
(d) Right triangle