Question

question 12 | bcpss_course3_unit6
choose the correct button in the table to indicate whether each set of side lengths would form a right triangle.

	right triangle	not a right triangle
18, 80, 82	○	○
19, 23, 21	○	○
26, 10, 24	○	○

Explanation:

Step1: Recall Pythagorean Theorem

For sides $a \leq b \leq c$, check $a^2 + b^2 = c^2$

Step2: Test 5,5,10

$5^2 + 5^2 = 25 + 25 = 50$; $10^2 = 100$
$50
eq 100$, so not right triangle.

Step3: Test 18,80,82

$18^2 + 80^2 = 324 + 6400 = 6724$; $82^2 = 6724$
$6724 = 6724$, so right triangle.

Step4: Test 19,21,23

$19^2 + 21^2 = 361 + 441 = 802$; $23^2 = 529$
$802
eq 529$, so not right triangle.

Step5: Test 10,24,26

$10^2 + 24^2 = 100 + 576 = 676$; $26^2 = 676$
$676 = 676$, so right triangle.

Answer:

1. 5, 5, 10: Not a Right Triangle
2. 18, 80, 82: Right Triangle
3. 19, 23, 21: Not a Right Triangle
4. 26, 10, 24: Right Triangle