Question

Please assist me with this problem​

Answer 1

Answer:

y = sqrt(5)

x = sqrt(10)

Step-by-step explanation:

y = sqrt(5)

Opposite angles are equal

x is the hypotenuse

x² = 5 + 5

x² = 10

x = sqrt(10)

Answer 2

Answers:

x = sqrt(10)

y = sqrt(5)

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Explanation:

Naturally I start with x as that letter precedes y in the alphabet; however, it's easier to start with y because it is a leg of this triangle. We will then use the value of y to find x later.

For any 45-45-90 triangle, the two legs are the same length. So that's why we're able to quickly see that y = sqrt(5)

To get the hypotenuse, we multiply the leg length by sqrt(2). This trick only works for 45-45-90 triangles.

hypotenuse = leg*sqrt(2)

x = sqrt(5)*sqrt(2)

x = sqrt(5*2)

x = sqrt(10)

The rule I used is sqrt(a)*sqrt(b) = sqrt(a*b)

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An alternate path is to use the pythagorean theorem to find x

a^2+b^2 = c^2

(sqrt(5))^2 + (sqrt(5))^2 = x^2

5 + 5 = x^2

10 = x^2

x^2 = 10

x = sqrt(10)