Answer:
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
