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liberstina [14]
3 years ago
7

(15 points)

Mathematics
1 answer:
Maslowich3 years ago
6 0

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}



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