Hi! First, we have to find the area of the larger right-triangle. We can do this by using the Pythagorean theorem; a^2+b^2=c^2.
(3+4)^2+6^2=C^2
7^2+6^2=c^2
49+36=C^2
85=C^2
C≈9.22
Now, because we know the triangles are similar, we can use scaling to find the length of the hypotenuse of the smaller triangle.
3/7(9.22)≈4
Finally, we plug it all in!
3^2+b^2=4^2
9+b^2=16
b^2=7
b≈2.64
Now, I did a lot of rounding in this because the numbers we're crazy. If my answer isn't correct, It will be very close.
