Answer:
B. 8m
Step-by-step explanation:
Given:
The figure is a kite having points QRST.
It has short diagonal QS.
Long diagonal RT
Diagonal Intersect at point P.
side QR = 10m
Diagonal QS = 12m
We need to find the length of segment RP.
According Diagonal Property of kite.
It states that Diagonals of Kite perpendicularly bisects each other.
QP = PS
RP = PT
But QS = QP + PS
QS = QP + QP
QS = 2 QP
QP = [tex]\frac{1}{2}[/tex] QS = [tex]\frac{1}{2}\times 12 = 6 m[/tex]
Now In Δ QPR
m∠ P = 90° (Diagonals of a kite is perpendicular to each other)
Now by Pythagoras theorem;
[tex]QR^2 = QP^2+RP^2\\RP^2 = QR^2 - QP^2\\RP^2 = (10)^2- (6)^2\\RP^2 = 100 -36\\RP^2=64\\RP = \sqrt{64} =8\ m[/tex]
Hence the Length of segment RP is 8m.
