Question

the hypotenuse and a side of a right angled triangle are 13cm and5cm respectively. fined the length of the third side​

Answer 1

Answer:

Lenght of the third side =12

Step-by-step explanation:

$hypotenuse = 13 \\ opposite = 5 \\ adjacent = x \\ {hyp}^{2} = {opp}^{2} + {adj}^{2}$

${13}^{2} = {5}^{2} + {x}^{2} \\ 169 = 25 + {x}^{2} \\ 169 - 25 = {x}^{2} \\ 144 = {x}^{2}$

$\sqrt{144} = \sqrt{ {x}^{2} } \\ 12 = x$

Answer 2

Answer:

If the third side is the hypotenuse, then (using the Pythagorean Theorem) the square of its length is the sum of the squares of the other two sides:  132+52 , so the length of the hypotenuse is √194=13.92838827718412...  

However, it is also possible to have a right triangle with a hypotenuse of 13 cm and one side of 5 cm, in which case the third side would be:  √132−542=12.  

Of course, the second answer may seem “nicer” but both are correct and the question is ambiguous.