Question

Find the length of hypotenuse of a triangle with sides of length \[\sqrt 5 \]m and \[3\sqrt 2 \]m.

Answer 1

Hint:A right-angled triangle with legs of lengths \[a\] and \[b\], and a hypotenuse of \[c\] has the lengths of its sides specified by the Pythagoras theorem as \[{c^2} = {a^2} + {b^2}\]. The Pythagorean Theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle. Any value unknown can be calculated by this formula.

Complete step by step solution:
The Pythagorean Theorem states that the area of the square whose side is the hypotenuse that is the side opposite the right angle is equal to the sum of the areas of the squares on the other two sides.
According to the question we need to find out the length of hypotenuse of the triangle whose two sides are given.
We know that, A right-angled triangle with legs of lengths \[a\]and\[b\], and a hypotenuse of \[c\] has the lengths of its sides specified by the Pythagoras theorem as \[{c^2} = {a^2} + {b^2}\].
For the given case \[a = \sqrt 5 m\] and \[b = 3\sqrt 2 m\]
Therefore,
\[{c^2} = {\left( {\sqrt 5 } \right)^2} + {\left( {3\sqrt 2 } \right)^2}\]
Squaring and adding we have,
\[
\Rightarrow 5 + 18 \\
\Rightarrow 23 \\
\]
Hence, the length of hypotenuse of a triangle with sides of length \[\sqrt 5 \]m and \[3\sqrt 2 \]m is\[\sqrt {23} \].

Note: Any right angled triangle if any of the side is unknown then the value of that side can be obtained by Pythagoras theorem. The theorem can be generalized in various ways to higher dimensional spaces, to spaces that are not Euclidean, to objects that are not right triangles and to objects that are not triangles at all but n-dimensional solids.