Given : - OP=(x+7)cm - OQ=(x+y)cm - OR=20cm - OS=16cm Concept used: Properties of a Parallelogram: - In a parallelogram, the diagonals bisect each other. This means that the diagonals PR and QS intersect at point O such that PO=OR and QO=OS. Calculation:
Since the diagonals bisect each other at O , we have: OP=OR, thus (x+7)=20 OQ=OS, thus (x+y)=16 From the equation (x+7)=20 : We solve for x:x=20−7=13 Next, we use the value of x to solve for y from the equation (x+y)=16 : Substitute x=13 into (x+y)=16 : 13+y=16 Solve for y:y=16−13=3 Finally, we calculate the value of (7y+5) : Substitute y=3 into (7y+5) : (7×3)+5=21+5=26 Thus, the value of (7y+5) is 26 .