CAT 2019 Geometry & Mensuration Question (Hard)

Question

If the rectangular faces of a brick have their diagonals in the ratio , then the ratio of the length of the shortest edge of the brick to that of its longest edge is

Accepted Answer

Step 1 Square both equations - - Step 2 Subtract equations to eliminate Step 3 Try simple values to get rational side ratios Let s assume - Then from Invalid Try Then From Then from So sides are , , Step 4 Ratio of shortest to longest edge Shortest Longest So required ratio Now simplify Try rational

CAT 2019

Quantitative

Geometry & Mensuration

Hard

If the rectangular faces of a brick have their diagonals in the ratio $3 : 2 \sqrt{3} : \sqrt{15}$ , then the ratio of the length of the shortest edge of the brick to that of its longest edge is

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