Question 465192
The hypotenuse of the smaller triangle is 5.


To find the hypotenuse of the larger triangle, note that the areas are in the ratio 4:5, with 4 corresponding to the smaller triangle. This is a two dimensional specification, so if we take the square root we will obtain the ratio of side lengths (one dimensional).


The ratio of the side lengths of the two triangles is 2:sqrt(5). Here we can build a ratio:


*[tex \LARGE \frac{2}{\sqrt{5}} = \frac{5 cm}{x cm}]


Solving, we get


*[tex \LARGE x = \frac{5\sqrt{5}}{2}].