# I have this problem with special triangles. I have read the lesson over and over again but I still can't seem to grasp it.Here are some sample questions that I don't understand: Find the length of...

I have this problem with special triangles. I have read the lesson over and over again but I still can't seem to grasp it.

Here are some sample questions that I don't understand:

Find the length of each leg.

Find BC

Find the exact perimeter of quadrilateral ABCD. AE=12, CE=20, AF=EC, AE=FC,.

Triangle PQR is a 30-60-90 triangle with right angle Q and longer leg PQ. Find the possible coordinates of R if P(-4,1) and Q(6,1). Hint: There are two solutions.

You don't have to give me the answers. I just want to know how to go about solving it.

gbeatty | Certified Educator

Special right triangles are special because their components have specific relationships. For example, a 30-60-90 degree triangle has a specific relationship between its length of sides. That means if you know one leg of the triangle, you can always find the other legs.

If you have the coordinates of R & Q (as you do), you can figure out how long RQ is, which is 10. You'd then have the length of the longer leg, and since the longer leg is twice the shorter leg, you'd know the shorter leg is 10 divided by the square root of 3. You'd calculate that, then count that distance up or down from Q to get the two possible points.

neela | Student

The given quadrilateral  is AECF , as per the measurement,

AE=12, EC=20, given. CF=AE=12 and FA=EC =20

Therefore, the perimeter= AE+EC+CF+FA=12+20+12+20=64 units.

To find coordinates of R:

The coordinates P qnd Q is known. By distance formula find PQ. Since PQ is known right angled triangle PQR, with angles P=30 and Q=90,  QR  must be  half the  PR.

See the Y  coordinates  of  P and Q . They are same. Therefore, PQ ||  to X axis.

Q being a right angle, QR must be || to Y axis . Therefore the the X cordinate of R remains the same as that of Q , Y cordinate of R is either  Y cordinate of Q  + (1/2)PR or Cordinate of Q - (1/2) PR.