Question

Please I need help

what is the value of x?
a.3√2 b.24 c.12√2 d.8
what is the value of y?
a.4√3 b.√3 c.12 d.10
what is the value of z?
a.12-4√3 b.12 c.6 d.15
​

Answer 1

x: C

y: A

z:

Explanation:

In a 45-45-90 triangle, the hypotenuse is larger than either of the legs by a factor of
`√(2)`. The length of x is therefore:

`12\cdot √(2)=12√(2)`

In a 30-60-90 triangle, the longer leg is larger than the shorter leg by a factor of
`√(3)`. Therefore:

`y=(12)/(√(3))=(12√(3))/(3)=4√(3)`

The hypotenuse of the 30-60-90 triangle is twice larger than the smallest leg, so it has a length of
`8√(3)`.

By the pythagorean theorem, you can find z+y:

`z+y=\sqrt{(12√(2))^2-12^2}=√(288-144)=12\\\\4√(3)+z=12 \\\\z=12-4√(3)`

Hope this helps!