Question

A side of an isosceles right angled triangle is 2cm, Find the length of its hypotenuse.​

Answer 1

Answer:

√8

Step-by-step explanation:

The question here states that: A side of an isoceles right angled triangle is 2 cm.

We've been asked to calculate the length of the hypotenuse.

Here we'll be using pythagoras theorem to calculate the length of hypotenuse.

Pythagoras theorem states that the square of the hypotenuse is equal to the sum of the square of other two sides in an right angled triangle. $\\\twoheadrightarrow\quad\sf{{Hypotenuse}^{2}={Opposite}^{2}+{Adjacent}^{2}}$

Equating value of opposite and adjacent as 2 cm.

$\twoheadrightarrow\quad\sf{{Hypotenuse}^{2}={2}^{2}+{2}^{2}}$

Equating value of 2² as 4.

$\twoheadrightarrow\quad\sf{{Hypotenuse}^{2}=4+4}$

Performing addition.

$\twoheadrightarrow\quad\sf{{Hypotenuse}^{2}=8}$

Transposing square from LHS to RHS in order to calculate the hypotenuse.

$\twoheadrightarrow\quad\underline{\boxed{\pmb{\frak{Hypotenuse=\sqrt{8}}}}}$

❝ Therefore, length of the hypotenuse of right angled isoceles triangle is √8. ❞