PQRS is a parallelogram in which PQ =(4x+ 1) cm, QR =26 cm, RS =25 cm and PS =(3y−1) cm.
Then, the value of (3x+ 2y) (in cm) is :

The correct option is 36.

Step-by-Step Explanation:
We are given a parallelogram $PQRS$ with the following side lengths:
• $PQ=(4x+1) \text{cm}$
• $QR=26 \text{cm}$
• $RS=25 \text{cm}$
• $PS=(3y-1) \text{cm}$

In any parallelogram, opposite sides are equal in length. Therefore, we have two pairs of equal sides:
1. $PQ=RS$
2. $PS=QR$

Step 1: Find the value of $x$

Using the property $PQ=RS$:

$4x+1=25$

Subtract $1$ from both sides:

$4x=25-1$

$4x=24$

Divide by $4$:

$x=6$

Step 2: Find the value of $y$

Using the property $PS=QR$:

$3y-1=26$

Add $1$ to both sides:

$3y=26+1$

$3y=27$

Divide by $3$:

$y=9$

Step 3: Calculate the value of $(3x+2y)$

Substitute $x=6$ and $y=9$ into the expression:

$3x+2y=3\left(6\right)+2\left(9\right)$

$3x+2y=18+18$

$3x+2y=36$

Thus, the value of $(3x+2y)$ is 36 cm.