Answer:
Given the statement: Kite QRST has a short diagonal of QS and a long diagonal of RT. The diagonals intersect at point P.
Properties of Kite:
It is given that: Side QR = 5m and diagonal QS = 6m.
Then, by properties of kite:
[tex]QP = \frac{1}{2}QS[/tex]
Substitute the value of QS we get QP;
[tex]QP = \frac{1}{2}(6)[/tex] = 3 m
Now, in right angle [tex]\triangle RPQ[/tex]
Using Pythagoras theorem:
[tex]QR^2= RP^2 +QP^2[/tex]
Substitute the given values we get;
[tex](5)^2= RP^2 +(3)^2[/tex]
or
[tex]25= RP^2 +9[/tex]
Subtract 9 from both sides we get;
[tex]16= RP^2[/tex]
Simplify:
[tex]RP = \sqrt{16} = 4 m[/tex]
Therefore, the length of segment RP is, 4m
Answer:
[tex]PR=4m[/tex]
Step-by-step explanation:
Firstly, we will draw diagram for kite
we are given
QR=5m
QS=6m
we know that QPR is a right angled triangle
so, QP=PS
[tex]QP=\frac{1}{2} QS[/tex]
[tex]QP=\frac{1}{2}\times 6[/tex]
[tex]QP=3[/tex]
now, we can use Pythagoras theorem
[tex]QR^2=QP^2+PR^2[/tex]
now, we can plug values
[tex]5^2=3^2+PR^2[/tex]
[tex]PR=4[/tex]
