Question

the diagonals of rectangle qrst intersect at p. given that ( mangle pts = 34^circ ) and ( qs = 10 ), find ( qp ).

( qp = square )

Explanation:

Step1: Recall properties of rectangle diagonals

In a rectangle, the diagonals are equal in length and bisect each other. So, \( QS = RT \) and \( QP = PS = PT = PR \), and \( QS = QP + PS = 2QP \) (since \( QP = PS \)).

Step2: Calculate QP

Given \( QS = 10 \), from the relationship \( QS = 2QP \), we can solve for \( QP \) by dividing both sides by 2: \( QP=\frac{QS}{2} \). Substituting \( QS = 10 \), we get \( QP=\frac{10}{2}=5 \).

Answer:

\( 5 \)