Question

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.

Answer 1

8m

Explanation:

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.

6m

8m

10m

12m

Odyssey

Answer 2

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