Question

(15 points)

Answer 1

Answer:

Each of the legs of isosceles right triangle is 5$\sqrt{3}$

Step-by-step explanation:

Watch the attached figure for the isosceles right angled triangle

Looking at the figure we see that AB=5√6 and BC=CA

According to the Pythagorean theorem the square of the hypotenuse is equal to the sum of the squares of the other two sides of a right triangle.

1) Applying the Pythagorean theorem to the isosceles right triangle, we have

$BC^{2} + CA^{2} = AB^{2}$

2) Let BC=a and CA=a as they both are equal

So,

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

=> $2a^{2} = (5\sqrt{6} )(5\sqrt{6} )$

=> $2a^{2} = 5*5*\sqrt{6}*\sqrt{6}$

=> $2a^{2} = 25*6$ (since √6*√6 = (√6)²= 6)

=> $2a^{2} = 150$

3) Dividing both sides by 2, we get

$\frac{2a^{2} }{2} =\frac{150}{2}$

4) Cancelling out the 2's on the left, we get

$a^{2}$ = 75

5) Taking the square root on both sides, we have

$\sqrt{a^{2}} = \sqrt{75}$

=> a = 5$\sqrt{3}$

So,

Each of the legs of isosceles right triangle is 5$\sqrt{3}$