ACDE ~ APQR. CD = 9 m, EC - 15 m, PQ = 15 m. What is the
length of R.P?
The length of R.P can be found by using the Pythagorean theorem twice.
First, we have CD = 9 m and EC = 15 m.
Using the Pythagorean theorem, we can find the length of AC, which is the hypotenuse of triangle ACD:
AC^2 = AD^2 + CD^2
AC^2 = 15^2 + 9^2
AC^2 = 225 + 81
AC^2 = 306
AC = √306
Since AC = DE (opposite sides of a parallelogram are equal), we have DE = √306.
Next, we have PQ = 15 m and DE = √306.
Using the Pythagorean theorem, we can find the length of DP, which is the hypotenuse of triangle DPE:
DP^2 = DE^2 + EP^2
DP^2 = (√306)^2 + 15^2
DP^2 = 306 + 225
DP^2 = 531
DP = √531
Finally, we have RP = DP - DR, where DR = EC = 15 m.
RP = √531 - 15
Therefore, the length of R.P is approximately √531 - 15 meters.