Desperately need help!
PQR is a right angled triangle with PR = 3cm and QR = 4cm. The square STUV is inscribed in triangle PQR. What is the length, in centimeters of the side of the square.
Please help!! and tell me how you did it..
This is my first post in the forum, and
I'm here to provide an extremely complicated method.
I'll get you an easier one later.
Be noticed that the units are all omitted.
As illurstrated we know that
By applying the Pythagoras' theorem in the right-angled triangle,
we obtain that
Then we assume the length of the side to be .
In , we can see that
Simplification of the equations above gives that
Similarly, in , calculation gives that
Considering that the segment and the segment are parallel, we know that,
Then we may see that
which gives that,
By doing all the calculations above we see that
By solving the equations we finally obtain that
Okay here it comes the easier one.
At first we need to find the length of .
My work above gives that
Obviously segments and are parallel, thus
Assume the length of the segment to be , then it naturally satisifies that equals to .
Hence, we obtain that
which gives that
Therefore, the length of the side equals to
Thanks for all your answers!
alexmahone you wrote this:
How do you know RO is 3?
Do you mean you make it up? You said that half times 5 times RO (the extra line you added) is the area.
What I don't understand it where the value of RO came from? You substituted 3 for RO but how did that get there?
The solutions you've been given are fine, but look a bit complicated, and most have left quite a bit of the working out. May I suggest a simpler way of setting out the answer?
Originally Posted by jgv115
Basically, all four of the triangles are right-angled triangles. This means, for example, that the longest side of any of them is of the shortest, the middle-sized side is of the longest, and so on. So, if we call the length of the sides of the square cm, we can work around the various triangles to get an equation for , like this:
So if we now add up the three lengths along :
Multiply both sides of this equation by :