CAT 2018 Ratio, Proportion and Variation Question (Medium)

Question

The area of a rectangle and the square of its perimeter are in the ratio 1 25. Then the lengths of the shorter and longer sides of the rectangle are in the ratio

Accepted Answer

Step 1 Let the sides of the rectangle be and . Area Perimeter Square of perimeter Given Step 2 Cross-multiplying gives Step 3 Let , where Then Substitute into equation Cancel from both sides Step 4 Expand right-hand side Bring all terms to one side Step 5 Solve the quadratic So or Take since Step 6

CAT 2018

Quantitative

Ratio, Proportion and Variation

Medium

The area of a rectangle and the square of its perimeter are in the ratio 1 : 25. Then the lengths of the shorter and longer sides of the rectangle are in the ratio

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