Question

If the legs of a 45º-45º-90º triangle have a length of 8 centimeters, what is the perimeter of the triangle?

Answer 1

The perimeter of the triangle is 27.31 cm.

Step-by-step explanation:

Given,

Length of 1st side = 8 cm

Since the given triangle is an isosceles right angled triangle.

So Length of 2nd side = Length of 1st side = 8 cm

Now we use the Pythagoras theorem to calculate the 3rd side.

"The square of the hypotenuse is equal to the sum of the squares of other two sides".

$\textrm{Length of 3rd side}=\sqrt{8^2+8^2}=\sqrt{64+64}=\sqrt{128}=8\sqrt{2}\ cm$

Now perimeter is equal  to the sum of all sides of the triangle.

Perimeter = Length of 1st side+Length of 2nd side+Length of 3rd side

Perimeter =$8+8+8\sqrt2=16+11.31=27.31\ cm$

Hence The perimeter of the triangle is 27.31 cm.