Which of the following sets of sides form a right-angled triangle?”
Which of the following sets of sides form a right-angled triangle?”
निम्नलिखित में से कौन सी भुजाएँ समकोण त्रिभुज की हैं?
Detailed Solution & Logic
12 cm, 16 cm, 20 cm
To check a right-angled triangle, we use the Pythagoras theorem:
$ a^2 + b^2 = c^2 $ (where ccc is the largest side)
Option 1: 16 cm, 31 cm, 34 cm
$16^2 + 31^2 = 256 + 961 = 1217$
$34^2 = 1156$
❌ Not equal → Not a right triangle
Option 2: 12 cm, 16 cm, 20 cm
$12^2 + 16^2 = 144 + 256 = 400$
$20^2 = 400$
✅ Equal → Right-angled triangle
Option 3: 6 cm, 7 cm, 10 cm
$6^2 + 7^2 = 36 + 49 = 85$
$10^2 = 100$
❌ Not equal
Option 4: 5 cm, 11 cm, 13 cm
$5^2 + 11^2 = 25 + 121 = 146$
$13^2 = 169$
❌ Not equal
Final Answer:
12 cm, 16 cm, 20 cm ✔️
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