Pls help. Find radicals in simplest form find missing side lengths

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

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.

correct answer is b. 27/8

step-by-step explanation: