Sketch the following to answer the question. kite qrst has a short diagonal of qs and a long diagonal of rt. the diagonals intersect at point p. side qr = 10m and diagonal qs = 12m. find the length of segment rp.

Short Answer RP = 8 meters.
Remark
A kite's diagonals bisect each other. (1/2) QS = QP. 
Another fact about a kite is that the diagonals meet at right angles. 
ΔQPR is a right triangle. 

Step One
Find QP
QP = 1/2 QS
QS = 12               Given
QP = 1/2 12
QP = 6

Step Two
Find RP
Use the Pythagorean Theorem To solve for RP

Givens
QP = 6        From Step 1
QR = 10     Given
QP = ??

We are dealing with a right angle triangle.
RP^2 + QP^2 = QR^2
RP^2 + 6^2 = 10^2
RP^2 + 36 = 100        Subtract 36 from both sides.
RP^2 = 100 - 36
RP^2 = 64                  Take the square root of both sides.
sqrt(RP^2) =sqrt(64)  
RP = 8 <<<<<<<< Answer