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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.

Respuesta :

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


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Answer:

Step-by-step 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

[tex](QR)^{2}=(RP)^{2}+(QP)^{2}[/tex]

[tex](5)^{2}=(3)^2+(RP)^2[/tex]

[tex]25=9+(RP)^2[/tex]

[tex]25-9=(RP)^2[/tex][tex]16=(RP)^2[/tex]

[tex]RP=4m[/tex]

Therefore,  the length of segment RP is 4m.

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