Question

The length of a rectangle is 16 centimeter and its perimeter is equal to the perimeter of a square with side 12.5 centimeter. Find the area of the rectangle.

Answer 1

- Hint: To solve this question, firstly we must find the perimeter of the square. After that, as the perimeter of the square and the rectangle is the same, we will be able to calculate the breadth of the rectangle. And then, lastly, we will calculate the area of the rectangle.
Let us first know the formulas that are used to calculate the area and perimeter of square and rectangle.
PERIMETER OF SQUARE: \[Length\text{ }of\text{ }one\text{ }side\text{ }\times \text{ }4\]
AREA OF SQUARE: \[Length\text{ }of\text{ }side\text{ }\times \text{ }Length\text{ }of\text{ }side\]
PERIMETER OF RECTANGLE: 2 (Length + Breadth)
AREA OF RECTANGLE: \[Length\text{ }\times \text{ }Breadth\]

Complete step-by-step solution -

The length of a rectangle is 16 centimeter and its perimeter is equal to the perimeter of a square with side 12.5 centimeter. Find the area of the rectangle.
Length of one side of a square = 12.5 centimeter
Perimeter of the square = \[Length\text{ }of\text{ }one\text{ }side\text{ }\times \text{ }4\]
                                                       = \[12.5\times 4\]
                                                       = 50 centimeter
Length of rectangle = 16 centimeter
Perimeter of rectangle = Perimeter of square
                                                       = 50 centimeter
Let the breadth of the rectangle be ‘x’.
2 (Length + Breadth) = 50 centimeter
2 (16 + x) = 50
32 + 2x = 50
2x = 50 – 32
x = \[\dfrac{18}{2}\]
x = 9
Therefore, the breadth of the rectangle is 9 centimeter.
Length of rectangle = 16 centimeter
Breadth of the rectangle = 9 centimeter
Area of the rectangle = \[Length\text{ }\times \text{ }Breadth\]
                                                         = \[\left( 16\text{ }\times \text{ }9 \right)\]
                                                         = 144
Therefore, the area of the square is 144 sq cm.

Note:-Let us now know about the formula to calculate the perimeter of some other shapes.
EQUILATERAL TRIANGLE: 3 \[\times \] a, where ‘a’ stands for the length of each side of the triangle.
ISOSCELES TRIANGLE: 2a + b, where ‘a’ stands for the length of the two equal sides and ‘b’ stands for the third unequal side.
SCALENE TRIANGLE: a + b + c, where ‘a’ stands for the length of the first side, and ‘b’ and ‘c’ are the lengths of the third and fourth sides respectively.
CIRCLE: \[2\pi r\]
One must do all the calculations very carefully for solving this question.
Also, not only in this question, one must be very careful while doing such questions as if there is any mistake in the calculations, the answer can come out to be wrong.