Which method should we use to solve the problem?
We can draw a model, but there are many units to be drawn since we need to draw a model to represent the perimeter too.
So, let’s just use the unitary method.
For the first part, we need to find the ratio of the breadth of the rectangle to its perimeter.
We are told that the breadth of the rectangle is two-ninths of its length.
This means the ratio of the breadth to the length
is 2 to 9.
So, 2 units represent the breadth
and 9 units represent the length.
We do not have the number of units representing the perimeter of the rectangle.
But, remember that the perimeter of a rectangle is equal to length plus breadth plus length plus breadth.
Hence, the perimeter is represented by
2 plus 9 plus 2 plus 9
which is equal to 22 units.
The ratio of the breadth to the perimeter
is 2 to 22.
This can be simplified to
1 to 11.
Therefore, the ratio of its breadth to its perimeter is 1 to 11.
Next, part (b) – How long is its breadth?
We know that the perimeter of the rectangle is 60 centimetres longer than its breadth.
So, we need to find the number of units representing the difference between the perimeter and the breadth.
Using the ratio of the breadth to the perimeter found in part (a),
the difference between the perimeter and the breadth is represented by
11 minus 1
which is equal to 10 units.
Thus, 10 units represent
60 centimetres.
And, 1 unit represents
60 divided by 10
which is equal to 6 centimetres.
Hence, the breadth of the rectangle is 6 centimetres.
Lastly, part (c) – What is the area of the rectangle?
To find the area of the rectangle, we need the length and the breadth.
We have found the breadth earlier.
Let’s find the length.
The ratio of the breadth to the length is 2 to 9
and the breadth is 6 centimetres.
So, 2 units represent 6 centimetres.
1 unit represents
6 divided by 2
which is equal to 3 centimetres.
And, 9 units represent
3 times 9
which is equal to 27 centimetres.
The area of the rectangle which is equal to length times breadth
is given by 27 times 6.
This works out to 162.
Therefore, the area of the rectangle is 162 square centimetres.