Question

can three line segments with the given lengths form a right triangle?
drag each set of lengths into the correct box.
12, 35, 37
16, 30, 34
18, 24, 42
20, 21, 29
yes
no

Explanation:

Step1: Apply Pythagorean theorem

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

Step2: Test 12, 35, 37

Calculate $12^2 + 35^2 = 144 + 1225 = 1369$, $37^2 = 1369$. So $12^2 + 35^2 = 37^2$.

Step3: Test 16, 30, 34

Calculate $16^2 + 30^2 = 256 + 900 = 1156$, $34^2 = 1156$. So $16^2 + 30^2 = 34^2$.

Step4: Test 18, 24, 42

Calculate $18^2 + 24^2 = 324 + 576 = 900$, $42^2 = 1764$. So $18^2 + 24^2
eq 42^2$.

Step5: Test 20, 21, 29

Calculate $20^2 + 21^2 = 400 + 441 = 841$, $29^2 = 841$. So $20^2 + 21^2 = 29^2$.

Answer:

Yes: 12, 35, 37; 16, 30, 34; 20, 21, 29
No: 18, 24, 42