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
(b) 10, 11, 15	o	o	o
(c) 10, 26, 28	o	o	o
(d) 6, 8, 10	o	o	o

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Check (a) 21, 28, 35

\(21^{2}+28^{2}=441 + 784=1225\), and \(35^{2}=1225\). Since \(21^{2}+28^{2}=35^{2}\), it is a right - triangle.

Step3: Check (b) 10, 11, 15

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

Step4: Check (c) 10, 26, 28

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

Step5: Check (d) 6, 8, 10

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

Answer:

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