Question

Find the value of each variable ​

Answer 1

Answer:

x = 12$\sqrt{2}$

y = 12

z = 12$\sqrt{3}$

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

Answer 2

Answer:

x = $12\sqrt{2}$ units

y = 12 units

z = $12\sqrt{3}$ 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: $1:\sqrt{3} :2$. Here, the hypotenuse is 24 and z is the longest leg, so we have the proportion:

$\frac{\sqrt{3} }{2} =\frac{z}{24}$

Cross-multiply:

$24\sqrt{3} =2z$

z = $12\sqrt{3}$ 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: $1:1:\sqrt{2}$. 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 $\sqrt{2}$: 12 * $\sqrt{2}$ = $12\sqrt{2}$ units

Hope this helps!