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= 6m. Find the length of segment RP

Answer 1

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:

• The diagonals are perpendicular

• Two disjoint pairs of consecutive sides are congruent by definition of kite

• One diagonal  is the perpendicular bisector to the other diagonal.

It is given that: Side QR = 5m and diagonal QS = 6m.

Then, by properties of kite:

$QP = \frac{1}{2}QS$

Substitute the value of QS we get QP;

$QP = \frac{1}{2}(6)$ = 3 m

Now, in right angle $\triangle RPQ$

Using Pythagoras theorem:

$QR^2= RP^2 +QP^2$

Substitute the given values we get;

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

or

$25= RP^2 +9$

Subtract 9 from both sides we get;

$16= RP^2$

Simplify:

$RP = \sqrt{16} = 4 m$

Therefore, the length of segment RP is, 4m

Answer 2

Answer:

$PR=4m$

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

$QP=\frac{1}{2} QS$

$QP=\frac{1}{2}\times 6$

$QP=3$

now, we can use Pythagoras theorem

$QR^2=QP^2+PR^2$

now, we can plug values

$5^2=3^2+PR^2$

$PR=4$