# Dimensions of a triangle formed from another right angled triangle

• Apr 23rd 2011, 12:12 AM
Timmy
Dimensions of a triangle formed from another right angled triangle
Hi Everyone,
A right angled triangle has a base of AC, the vertical is AB and the hypotenuse is BC.
Draw a line parallel to the base, from BC/2 intersecting vertical AB.
How can I find the lengths of the base and vertical of this smaller right angled triangle?
Thanks.
• Apr 23rd 2011, 12:27 AM
HappyJoe
First thing to do is to notice that the two triangles are similar. To do this, you could argue that their angles are pairwise equal.

Then you need to apply what you know about similar triangles, namely that the ratio between a pair of corresponding sides is always the same, no matter which pair you consider. In particular, you know that the ratio between the hypotenuse of the big triangle and the hypotenuse of the small triangle is 2.

Hope this helps. Otherwise, feel free to ask again.
• Apr 23rd 2011, 01:37 AM
Timmy
Somehow missed considering the ratios.
Calculating a few triangles now.