PQRS is a parallelogram whose diagonals PR and QS intersect at a point O such…
2024
PQRS is a parallelogram whose diagonals PR and QS intersect at a point O such that OP = (x + 7) cm, OQ = (x + y) cm, OR = 20 cm and OS = 16 cm. Then, value of (7y + 5) (in cm) is :
- A.
21
- B.
23
- C.
26
- D.
28
Show answer & explanation
Correct answer: C
In a parallelogram, the diagonals bisect each other at their point of intersection — that is, the intersection point is the midpoint of both diagonals, so each diagonal splits into two equal segments. Applying this to parallelogram PQRS with diagonals PR and QS intersecting at O:
O is the midpoint of diagonal PR, so OP = OR: x + 7 = 20, giving x = 13.
O is the midpoint of diagonal QS, so OQ = OS: x + y = 16. Substituting x = 13 gives 13 + y = 16, so y = 3.
Evaluate the required expression: 7y + 5 = 7(3) + 5 = 21 + 5 = 26.
Checking back: with x = 13, OP = x + 7 = 20, which equals OR; and with y = 3, OQ = x + y = 16, which equals OS. Both bisection conditions are satisfied, confirming the values of x and y.
So the value of (7y + 5) is 26 cm.