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

3 m
4 m
5 m
6 m

Answer 1

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)²16= (RP)²

RP= 4m

Therefore, the length of segment RP is 4m.

Explanation:

Answer 2

The length of RP is 4 m.

Since a kite is symmetric about one of its diagonals, then the other diagonal bisects that one. Additionally, the diagonals are perpendicular to each other. This forms two right triangles inside of the kite.

The bottom leg of the right triangle will be 3 (half of the diagonal) and the hypotenuse will be 5. We will use the Pythagorean theorem to answer this:

3²+b²=5²
9+b²=25

Subtract 9 from both sides:
9+b²-9=25-9
b²=16

Take the square root of both sides:
√(b²) = √16
b=4