Question

What is the length of the longest side of a right-angled triangle whose other two sides are 10 m and 5 m long?

• A. $\sqrt{5}$ m
• B. $4\sqrt{5}$ m
• C. $5\sqrt{5}$ m
• D. $5\sqrt{4}$ m

Answer 1

The correct option is C $5\sqrt{5}$ m

In a right-angled triangle, the longest side is its hypotenuse.
Also, in such a triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
$\therefore$ Using Pythagoras' Theorem, we get that the hypotenuse equals $\sqrt{{10}^2+5^2}.$
$\Rightarrow \text{Hypotenuse}=\sqrt{100+25}$ $=\sqrt{125}$
$=5\sqrt{5}\text{m}$

Therefore, the length of the hypotenuse is $5\sqrt{5}$ m.