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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.

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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.

This problem has been solved

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