High school math tip: learn how to apply the ratios 1:1:√2 for the 45/45/90 right triangle and 1:√3:2 for the 30/60/90 triangle; these two triangles probably constitute 90% of the examples and problems you'll see.
He we have half a square, the 45/45/90 isosceles right triangle, sides in ratio 1:1:√2. We write that ratio for our sides and solve.
1:1:√2 = (3/2)√2 : y : x
Ratios are pretty much like fractions, and we can make fraction equations out of corresponding pairs:
1/1 = ( (3/2)√2 ) / y
y = (3/2)√2
1 /√2 = (3/2)√2 / x
x = (3/2)√2 × √2 = (3/2)(2) = 3
Answer: y = (3/2)√2, x = 3
It's not too hard to get fast at these and just say y=(3/2)√2 because it's an isosceles triangle and x = y×√2 = 3 for the hypotenise.
