Find the value of each variable

x = 12

y = 12

z = 12

Step-by-step explanation:

The triangle with z as one of it's sides is a 30, 60, 90 triangle where the longest side of the triangle is 2x, the shortest side as x, and the middle side as x*sqrt of 3.

The shared line between the two triangle is 12 and z is 12*sqrt of 3

The left triangle is a 45, 45, 90 triangle where the 2 sides that look the same are the same and the hypotenuse is x sqrt of 2 so y is 12 and x is 12 sqrt of 2

x = units

y = 12 units

z = units

Step-by-step explanation:

Notice that the biggest triangle is broken up into a 45-45-90 isosceles triangle with hypotenuse x and leg y, as well as a 30-60-90 triangle with hypotenuse 24 and long leg z.

Let's focus on finding z first. Remember that in a 30-60-90 triangle, the ratio of the short leg to the long leg to the hypotenuse is: . Here, the hypotenuse is 24 and z is the longest leg, so we have the proportion:

Cross-multiply:

z = units

Now, let's find the smallest leg of the 30-60-90 triangle; it is simply 24/2 = 12 units. Let's move onto x and y.

Remember that in a 45-45-90 triangle, the ratio of one leg to the second leg to the hypotenuse is: . So, since y is a leg of this triangle and the smallest leg of the 30-60-90 triangle coincides with the second leg of the 45-45-90 triangle, y = 12 units.

Finally, x is found by multiplying 12 by : 12 * = units

Hope this helps!

whats the

the answer is 62.8 cubic units