So first we calculate the weekly hours:
23.80 x 34 = 809.20
Then we calculate the time and half:
23.80 x 6 x 1.5 = 214.2
Then we total then together:
214.2 + 809.20 = 1023.40
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
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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
3/5 + 3/20
=12/20 + 3/20
=15/20
1 - 15/20
=20/20 - 15/20
=5/20
=1/4
