Question

Find the leg of each isosceles right triangle when the hypotenuse is of the given measure. Given = 5 is the square root of 6

Answer 1

Answer:

$5\sqrt{3}=x$

Step-by-step explanation:

We are given an isosceles right triangle.

Refer the attached figure

ΔABC is an isosceles right triangle.

AB = BC = x (Let)

AC = Hypotenuse = 5√6 (Given)

Now using Pythagoras theorem

$Hypotenuse^2=Perpendicular^2+Base^2$

$AC^2=AB^2+BC^2$

$(5\sqrt{6})^2=x^2+x^2$

$150=2x^2$

$\sqrt{150}{2}=x^2$

$75=x^2$

$\sqrt{75}=x$

$5\sqrt{3}=x$

Hence the leg of each isosceles right triangle when the hypotenuse is 5√6 is $5\sqrt{3}$.

Answer 2

Hello : 
by the pytagore rule : 
the length of the  hypotenuse is x :  x²= (5√6)² +(5√6)²
x² = 300
x =√300