Question

each option below shows the lengths of three sides of a triangle. select the options that represent the lengths of the sides of a right triangle. select all that apply. □ 16, 30, 34 □ 9, 12, 15 □ 9, 26, 27 □ 41, 43, 59 □ 10, 24, 28 □ none of the options above are the lengths of the sides of a right triangle.

Explanation:

Step1: Check Pythagorean theorem for 16,30,34

Square each number: $16^2=256$, $30^2=900$, $34^2=1156$. Sum of smaller squares: $256+900=1156=34^2$

Step2: Check Pythagorean theorem for 9,12,15

Square each number: $9^2=81$, $12^2=144$, $15^2=225$. Sum of smaller squares: $81+144=225=15^2$

Step3: Check Pythagorean theorem for 9,26,27

Square each number: $9^2=81$, $26^2=676$, $27^2=729$. Sum of smaller squares: $81+676=757
eq729$

Step4: Check Pythagorean theorem for 41,43,59

Square each number: $41^2=1681$, $43^2=1849$, $59^2=3481$. Sum of smaller squares: $1681+1849=3530
eq3481$

Step5: Check Pythagorean theorem for 10,24,28

Square each number: $10^2=100$, $24^2=576$, $28^2=784$. Sum of smaller squares: $100+576=676
eq784$

Answer:

16, 30, 34
9, 12, 15