Question

How do you use the Pythagoras theorem to find the length of hypotenuse if one leg is $ 34\,cm $ and the other leg is $ 18\,cm $ ?

Answer 1

Hint: In the given problem, we are required to find the length of the hypotenuse of a right angled triangle one leg whose length is $ 34\,cm $ and other leg is $ 18\,cm $ . The problem requires us to have thorough knowledge of geometrical properties and ideas. Pythagoras theorem is one of the most basic geometrical tools that can be used to find a missing side of a right angled triangle easily.

Complete step-by-step answer:
First leg of right angled triangle $ = 34{\text{ }}cm $
Second leg of right angled triangle \[ = 18{\text{ }}cm\]
Using the Pythagoras theorem in the right angled triangle to find the missing side of the triangle, in this case the hypotenuse of the triangle, we get,
 $ {(Hypotenuse)^2} = (Altitude){}^2 + {(Base)^2} $
Putting the values of base and altitude of the triangle, we get,
 \[ \Rightarrow {(Hypotenuse)^2} = (34){}^2 + {(18)^2}\]
Calculating the squares of the terms, we get,
 \[ \Rightarrow {(Hypotenuse)^2} = (1156) + (324)\]
Taking square root on both sides of the equation in order to find the length of the diagonal,
 \[ \Rightarrow Hypotenuse = \sqrt {1480} \]
Simplifying the expression with square root, we get,
  \[ \Rightarrow Hypotenuse = 2\sqrt {370} \]
So, the length of the hypotenuse of the right angled triangle whose other two legs are given to us as $ 34\,cm $ and $ 18\,cm $ is $ 2\sqrt {370} {\text{ }}cm $ .
So, the correct answer is “ $ 2\sqrt {370} {\text{ }}cm $ ”.

Note: The length of the hypotenuse of a right angled triangle can also be found with the help of trigonometric ratios. Trigonometric ratios are the ratio of the sides of a right angled triangle and thus can be used to calculate the missing side of a triangle.