Sketch the following to help 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
<em>Givens</em> 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