Question

determine whether a triangle with the given side lengths is a right triangle.
side lengths\tright triangle\tnot a right triangle\tnot enough information
(a) 6, 8, 10\t○\t○\t○
(b) 10, 11, 15\t○\t○\t○
(c) 15, 36, 39\t○\t○\t○
(d) 10, 26, 28\t○\t○\t○

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, $a^2 + b^2 = c^2$, where $c$ is the longest side.

(a) 6, 8, 10:

Calculate squares of sides:
$6^2 = 36$, $8^2 = 64$, $10^2 = 100$
Check sum: $36 + 64 = 100$

(b) 10, 11, 15:

Calculate squares of sides:
$10^2 = 100$, $11^2 = 121$, $15^2 = 225$
Check sum: $100 + 121 = 221
eq 225$

(c) 15, 36, 39:

Calculate squares of sides:
$15^2 = 225$, $36^2 = 1296$, $39^2 = 1521$
Check sum: $225 + 1296 = 1521$

(d) 10, 26, 28:

Calculate squares of sides:
$10^2 = 100$, $26^2 = 676$, $28^2 = 784$
Check sum: $100 + 676 = 776
eq 784$

Answer:

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