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Question

Thank you for your help. Here is a link to the problem: Link to image of problem

Answer 1

If you re-draw the 3 triangles that are made, and put them side-by-side, you will see that this problem becomes easy:

Triangles 1 (the large blue one on the outside), 2 (the medium red on on the upper middle), and 3 (the smaller green one on the bottom middle) are similar triangles so their sides are proportional. Using Triangle #2 and Triangle #3, you can write proportional statements:

30 is to "x" like "x" is to 25 or:

30/x = x/25

Then cross multiply to get (30)(25) = x²

Then take the square root:

x = √(30•25)

Taking the square root of 25 gives you 5 so:

x = 5√30 cm

Answer 2

Hi Lia,

In order to answer this question, we need to remember right triangle altitude theorem, which tells us that the altitude on the hypotenuse is equal to the geometric mean of line segments formed by altitude to the hypotenuse.

So for this problem, we know that the line segments formed by the altitude to the hypotenuse have lengths of 25cm and 30cm.

In order to calculate the length of the hypotenuse, we need to find the geometric mean of those two segments:

This is done by multiplying the two numbers we were given, and then taking the square root of the product. Plugging in, we get:

geometric mean = √(25cm)(30cm)

= 5√30cm

Hope that helps!