Using what we know about right and similar triangles, we will see that x = 25.
How to find the hypotenuse of the largest triangle?
First, we can find the hypotenuse of the smallest triangle by using the Pythagorean theorem.
6^2 + 8^2 = H^2 = 100
H = √100 = 10
Then the perimeter of the smaller triangle is:
6 + 8 + 10 = 24
Now, the triangles are similar, then the perimeter of the larger triangle is "k" times the perimeter of the smaller triangle, so we can write.
60 = k*24
Where k is the scale factor between the triangles.
k = 60/24 = 30/12 = 10/4 = 5/2
Then, x will be 5/2 times the hypotenuse of the other triangle, this gives:
x = (5/2)*10 = 25
The value of x is 25.
If you want to learn more about right triangles:
https://brainly.com/question/2217700
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