The breadth and length of a rectangle are in the ratio 2 : 3. Also, if numerical values of the breadth, length and area of the rectangle are in a continued proportion, then find the area of the rectangle.
Question
The breadth and length of a rectangle are in the ratio 2 : 3. Also, if numerical values of the breadth, length and area of the rectangle are in a continued proportion, then find the area of the rectangle.
Solution
Let's assume that the breadth of the rectangle is 2x and the length is 3x, where x is a common factor.
According to the given information, the numerical values of the breadth, length, and area of the rectangle are in a continued proportion. This means that the ratio of the length to the breadth is equal to the ratio of the area to the length.
So, we have the equation:
(3x) / (2x) = (Area) / (3x)
Simplifying this equation, we get:
3 / 2 = Area / 3
Cross-multiplying, we have:
Area = (3/2) * 3
Area = 9/2
Therefore, the area of the rectangle is 9/2.
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