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Given below is a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. You should use the given data and your knowledge of Mathematics to choose between the possible answers. What will be the area of a rectangle? I. The ratio of length and breadth of rectangle is 12 : 7. II. Length is 5 cm lesser than the diagonal.

Given below is a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. You should use the given data and your knowledge of Mathematics to choose between the possible answers. What will be the area of a rectangle? I. The ratio of length and breadth of rectangle is 12 : 7. II. Length is 5 cm lesser than the diagonal. Correct Answer The data in both the statements I and II together is necessary to answer the question.

From statement I:

The ratio of length and breadth of rectangle is 12 : 7. Let the length be 12T and breadth be 7T.

Area = 12T × 7T, which cannot be found if T is not known.

∴ Statement I alone is not sufficient to answer the question.

From statement II:

Length is 5 cm lesser than the diagonal. Let diagonal length be N and length be (N - 5).

We know, diagonal length = √ (square of length + square of breadth)

But, we have two variables, breadth and N, hence breadth and length cannot be found, and hence the area.

∴ Statement II alone is not sufficient to answer the question.

From statements I and II together:

The ratio of length and breadth of rectangle is 12 : 7. Let the length be 12T and breadth be 7T.

Length is 5 cm lesser than the diagonal. Let diagonal length be (12T - 5).

We know, diagonal length = √ (square of length + square of breadth)

Using this equation, we can solve for variable T, and find area.

Area = 12T × 7T

∴ Using both the statements together, we can answer the given question.

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