Prove that this is a right triangle, show work sides 2√5 2√5 2√10

The triangle has sides a,b,c such that

a = 2*sqrt(5), b = sqrt(5), and c = 2*sqrt(10)

Square each value

a = 2*sqrt(5)

a^2 = (2*sqrt(5))^2

a^2 = 2^2(sqrt(5))^2

a^2 = 4*5

a^2 = 20

b^2 = 20 for similar reasons as side 'a'

c = 2*sqrt(10)

c^2 = (2*sqrt(10))^2

c^2 = 2^2*(sqrt(10))^2

c^2 = 4*10

c^2 = 40

Using the pythagorean theorem, we see that

a^2 + b^2 = c^2

20 + 20 = 40

40 = 40

So the initial equation a^2 + b^2 = c^2 is true making the triangle with sides a,b,c defined above to be a right triangle

(2 * sq root 5)^2 = 20

20 + 20 = 40

2*sq root(10)^2 = 40

The sum of both sides squared = hypotenuse squared.

By the Pythagorean Theorem, we know that this is a right triangle.

Step-by-step explanation:

2.

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