Multiplication Identities - STD 9 - Page 80.1 EM
Rectangle Area Problem
Using Algebraic Identity
Problem
The perimeter of a rectangle is 40 cm and its area is 70 cm². Find the area of the rectangle when each side is shortened by 3 cm.
Original Rectangle
Perimeter = 40 cm → l + b = 20 cm
Area = 70 cm² → l × b = 70
Let length = l and breadth = b
New Rectangle
New length = l - 3
New breadth = b - 3
New Area = (l - 3)(b - 3)
Using Algebraic Identity
We know that:
(l - 3)(b - 3) = lb - 3(l + b) + 9
Substitute the known values:
= 70 - 3(20) + 9
= 70 - 60 + 9
= 19
New Area
19 cm²