Find the missing side lengths, leave your answers as radical in simplest form. ( Please answer ASAP!)

9) a = 8, b = 4√2

10) x = 7√2, y = 7

11) x = 5√2, y = 5

12) a = 10, b = 5√2

Step-by-step explanation:

You can notice all these triangles are special as 45° - 45° - 90° triangles. In 45° - 45° - 90° triangles, the hypotenuse is √2 times the sides. We can set up these equations and solve:

9)

a = 4√2 * √2

a = 8

Since the triangle is isosceles, the legs are the same length, so:

b = 4√2

10)

x = 7 * √2

x = 7√2

Since the triangle is isosceles, the legs are the same length, so:

y = 7

11)

x = 5 * √2

x = 5√2

Since the triangle is isosceles, the legs are the same length, so:

y = 5

12)

a = 5√2 * √2

a = 10

Since the triangle is isosceles, the legs are the same length, so:

b = 5√2