A right isosceles triangle has side lengths of 13.2, 13.2, and 18.6
meters. What is the hypotenuse of a similar triangle with legs 4.4
meters in length?
The ratio of the sides in similar triangles is constant. Therefore, we can set up the following proportion:
$\frac{13.2}{18.6}=\frac{4.4}{x}$
Cross-multiplying gives:
$13.2x=4.4\cdot 18.6$
Dividing both sides by 13.2 gives:
$x=4.4\cdot \frac{18.6}{13.2}$
Doing the multiplication and division gives:
$x\approx 6.2$
Therefore, the hypotenuse of the similar triangle is $\boxed{6.2}$ meters in length.