Question

How do you find the length of each leg of an isosceles right triangle whose hypotenuse is $14cm$ ?

Answer 1

Hint: In the question above, we have an isosceles right-angled triangle, and the measurement of the hypotenuse. We all are aware of the Pythagoras theorem, which involves the hypotenuse value when a triangle has a right angle. With the help of this theorem, we can easily find the value of the two sides.
The formula goes like,
${(sid{e_1})^2} + {(sid{e_2})^2} = {(Hypotenuse)^2}$

Complete step-by-step solution:
As per the question, the hypotenuse of the given triangle is $14cm$ , and we all know that the hypotenuse is the longest side and the other sides of the triangle if have the same lengths, the triangle becomes isosceles, automatically.
The angles of the triangle are also of the measures $45^\circ - 45^\circ - 90^\circ $
By Pythagoras theorem we already know that ${(sid{e_1})^2} + {(sid{e_2})^2} = {(Hypotenuse)^2}$
Let us assume the length of the side to be $x$ ,
So, now if both the sides are equal, the equation will be written as,
$ \Rightarrow {x^2} + {x^2} = {(14)^2}$
Adding the similar variables and also, calculating the squares of required variables,
$ \Rightarrow 2{x^2} = 196$
Taking the constants on the other side,
$ \Rightarrow {x^2} = \dfrac{{196}}{2}$
Dividing the numbers,
$ \Rightarrow {x^2} = 98$
Taking square roots on both sides,
$ \Rightarrow x = \sqrt {49 \times 2} $
Taking out the number which has a square root,
$ \Rightarrow x = 7\sqrt 2 $

Therefore, the side of a right-angled triangle with a hypotenuse as $14cm$ is going to be $7\sqrt 2 $ cm.

Note: A hypotenuse side is the longest side of a triangle. A hypotenuse basically is in front of the right angle of the triangle, and is always to the opposite side of the angle with the measurement of $90^\circ $ . A Pythagoras theorem involves the two sides and the hypotenuse of the right-angled triangle, and tells that the addition of the squares of the sides is equal to the square of the hypotenuse.