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 = 5m and diagonal QS = 6m. Find the length of segment RP.

Answer 1

Adjacent sides of kite are equal and diagonal intersects at 90 so it will bisect the other diagonal

according to pythagorean theorm
hy^2=l^2+b^2
5^2-3^2=b^2
25=9=b^2
b=4
RP=4 m

Answer 2

Explanation:

Given: Kite QRST has a short diagonal of QS and a long diagonal of RT. The diagonals intersect at point P. Side QR = 5m and diagonal QS = 6m.

Since, diagonals of kite bisect each other, thus QP=6m

Now, in ΔPQR, we have

`(QR)^(2)=(RP)^(2)+(QP)^(2)`

`(5)^(2)=(3)^2+(RP)^2`

`25=9+(RP)^2`

`25-9=(RP)^2`
`16=(RP)^2`

`RP=4m`

Therefore, the length of segment RP is 4m.