Answer :
The area of the rectangle is 54 square cm or 54 cm².
Given that: Length of the rectangle is 3 cm longer than its width. The perimeter of a rectangle is 30cm. To find the area of the rectangle.
What is a rectangle?
A rectangle is a closed figure which is a parallelogram whose length of the opposite sides is equal and the angle between each of its edges is a right angle or it is a right-angled parallelogram whose length of the opposite sides is equal.
Let the length of the rectangle be l and the breadth of the rectangle be b.
As per the question: length is 3 cm longer than width.
Therefore, the length of the rectangle = b + 3
Length of the rectangle = b + 3
Width of the rectangle = b
The formula for the perimeter of a rectangle is given:
P = 2 × (l + b). where
l = length of the rectangle
b = breadth of the rectangle
P = perimeter
given perimeter in the question P = 30 cm
Putting values of l, b, and P in the equation.
30 = 2 × ((b + 3) + b)
=> 30 = 2 × (b + 3 + b)
Dividing both sides by 2:
30 / 2 = 2 × (b + 3 + b) / 2
=> 15 = 2b + 3
or 2b + 3 = 15
Subtracting both sides by 3:
2b + 3 - 3 = 15 - 3
2b = 12
Dividing both sides by 2:
2b / 2 = 12 / 2
b = 6
The width of the rectangle is b = 6 cm
The length of the rectangle is (6 + 3) cm, l = 9 cm
Therefore, the width is 6 cm and the length is 9 cm.
The area of the rectangle is given by the formula:
A = l × b where,
A = area
l = length of the rectangle
b = breath of the rectangle
Putting values of l and b in the equation, we get:
A = 9 × 6
= 54
Therefore, the area of the rectangle is 54 square cm or 54 cm²
Hence the area of the rectangle is 54 square cm or 54 cm².
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