Question

The two legs of a right triangle are equal and the square of its hypotenuse is 50. Find the length of each leg.

Answer 1

Hint: Let x be the length of two legs which are equal in length.
It is given that the square of the hypotenuse is 50. $\therefore {H^2} = 50$ .
Thus, find the length of two legs using Pythagoras’ theorem.

Complete step-by-step answer:
It is given that the legs of a right triangle are equal and the square of its hypotenuse is 50.
Let the length of the same legs of the right triangle be x.
So, by using the Pythagoras’ theorem, we can find the length of the same two legs.
The Pythagoras’ theorem is stated as, the square of hypotenuse is the sum of squares of the remaining two sides of the triangle.
 $\therefore {H^2} = {a^2} + {b^2}$
It is given that the square of the hypotenuse is 50. $\therefore {H^2} = 50$ and \[a = b = x\] .

 $
  \therefore 50 = {x^2} + {x^2} \\
  \therefore 2{x^2} = 50 \\
  \therefore {x^2} = 25 \\
  \therefore x = \pm 5 \\
 $
Here, x = -5 is not possible because x is the length of a side and length of a side cannot be negative.
Thus, \[x = 5\] .
Therefore, the length of each leg is 5 units.
Note: Pythagoras’ Theorem:
In a right angle triangle, the square of the hypotenuse is the sum of the squares of the remaining two sides.
Here, hypotenuse is the longest side of the triangle.
For example,

The Pythagoras’ theorem for the above diagram will be ${H^2} = {a^2} + {b^2}$ .