Question : If the hypotenuse of an isosceles right-angled triangle is 10 cm, then the other two sides (in cm) are __________.
Option 1: $10\sqrt{2}$ and $10\sqrt{2}$
Option 2: $8\sqrt{2}$ and $8\sqrt{2}$
Option 3: $6\sqrt{2}$ and $6\sqrt{2}$
Option 4: $5\sqrt{2}$ and $5\sqrt{2}$
Correct Answer: $5\sqrt{2}$ and $5\sqrt{2}$
Solution :
Given: Hypotenuse of the isosceles right-angled triangle = 10 cm
Let the other two equal sides be $x$ cm.
Now applying the Pythagoras theorem, we get,
$x^2+x^2=10^2$
⇒ $2x^2=100$
$\therefore x=\sqrt{50}=5\sqrt{2}$
Hence, the correct answer is $5\sqrt{2}$ and $5\sqrt{2}$.
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