The length of a rectangle is (P+3) cm and its breadth is (2P-5) cm. If its perimeter is 26 cm, then what is the area of the rectangle in cm²?

A) 13
B) 40
C) 48
D) 56

The area of the rectangle is calculated to be 40 cm² after finding the values of length and breadth using the given perimeter. Setting up the equation from the perimeter allowed us to solve for P, which led to the dimensions. The chosen multiple-choice option is B) 40.
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Answered by Anonymous | 2025-07-04

To find the area of the rectangle, we first need to determine the value of P using the given perimeter equation. The formula for the perimeter of a rectangle is:
Perimeter = 2 ( Length + Breadth )
Given:

Length = ( P + 3 ) cm
Breadth = ( 2 P − 5 ) cm
Perimeter = 26 cm

Substitute these values into the perimeter formula:
26 = 2 (( P + 3 ) + ( 2 P − 5 ))
Simplify the equation inside the brackets:
26 = 2 ( P + 3 + 2 P − 5 ) 26 = 2 ( 3 P − 2 )
Expand and solve for P :
26 = 6 P − 4 26 + 4 = 6 P 30 = 6 P P = 6 30 ​ P = 5
Now, substitute back to find the length and breadth:

Length = P + 3 = 5 + 3 = 8 cm
Breadth = 2 P − 5 = 2 ( 5 ) − 5 = 10 − 5 = 5 cm

The area of a rectangle is given by:
Area = Length × Breadth
Substitute the values:
Area = 8 × 5 = 40 cm 2
Therefore, the area of the rectangle is 40 cm².
The correct option is: B) 40

Answered by danjohnbrain | 2025-07-06