Answer:
Remember that for a triangle rectangle we have the Pythagorean's theorem, it says that the square of the hypotenuse is equal to the sum of the squares of the catheti.
Then if the catheti of a triangle rectangle are A and B, and the hypotenuse is H, we have:
H^2 = A^2 + B^2
In the smaller triangle we can see that:
H = 10
A = 6
Then:
10^2 = 6^2 + B^2
100 = 36 + B^2
100 - 36 = B^2
64 = B^2
√64 = B = 8
And we know that the perimeter of a triangle is equal to the sum of the lengths of it's sides, then the perimeter of the smaller triangle is:
P = 10 + 6 + 8 = 24
Now we know that the triangles are similar and related by a factor of 4/3, then each measurement of the larger triangle will be equivalent to 4/3 times the corresponding measurement of the smaller triangle, then if the measures of the larger triangle are A', B', and H', we can write these as:
A' = (4/3)*A = (4/3)*6 = 8
B' = (4/3)*B = (4/3)*8 = 10.67
H' = (4/3)*H = (4/3)*10 = 13.33
Then the perimeter of the larger triangle is:
P' = 8 + 10.67 + 13.33 = 32