Answer:
11 cm, 11 cm
Step-by-step explanation:
Let the length and width of the rectangle be x cm and y cm respectively.
Therefore,
Perimeter of rectangle = 44 cm
2(x + y) = 44
x + y = 44/2
x + y = 22...... (1)
Area of rectangle = xy
When length is increased by 4 cm and breadth is increased by 2 cm.
New length = (x + 4) cm
New width = (y + 2) cm
New area of rectangle = original area + 72.. (given)
Therefore,
(x + 4) (y + 2) = xy + 72
xy + 2x + 4y + 8 = xy + 72
2x + 4y = 72 - 8
2x + 4y = 66
2(x + 2y) = 66
x + 2y = 66/2
x + 2y = 33.... (2)
Subtracting equation (1) from equation (2)
x + 2y - (x + y) = 33 - 22
x + 2y - x - y = 11
y = 11
Substituting y = 11 in equation (1)
x + 11 = 22
x = 22 - 11
x = 11
Thus, the dimensions of the rectangle are 11 cm and 11 cm.
