CAT 2022 Geometry & Mensuration Question (Medium)

Question

The lengths of all four sides of a quadrilateral are integer valued. If three of its sides are of length 1 cm, 2 cm and 4 cm, then the total number of possible lengths of the fourth side is

Accepted Answer

Step 1 Let the sides of the quadrilateral be a 1 cm, b 2 cm, c 4 cm, d unknown side integer In any quadrilateral, the sum of the lengths of any three sides must be greater than the fourth side. So for each side 1. a b c d 1 2 4 7 d c 1 2 d 4 d 1 3. a c d b 1 4 d 2 always true for d 0 4. b c d a 2 4

CAT 2022

Quantitative

Geometry & Mensuration

Medium

The lengths of all four sides of a quadrilateral are integer valued. If three of its sides are of length 1 cm, 2 cm and 4 cm, then the total number of possible lengths of the fourth side is

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