Mathematics

Mathematics

Problem

Triangles GHI and JKL satisfy ∠G=∠J\angle G = \angle J. The sides including these angles are GH=8 cmGH = 8\,\text{cm}, GI=12 cmGI = 12\,\text{cm} and JK=10 cmJK = 10\,\text{cm}. If the triangles are similar by the SAS criterion, find the length of JLJL. a) 13 cm13\,\text{cm} b) 18 cm18\,\text{cm} c) 15 cm15\,\text{cm} d) 16 cm16\,\text{cm}
Intuitive explanation

This problem tests the SAS (Side-Angle-Side) similarity criterion: two triangles are similar if an included angle is equal and the sides forming that angle are proportional. Since ∠G=∠J\angle G = \angle J and you know all four sides around these angles, you need to set up the ratio of the sides at GG to the sides at JJ and use it to find the missing side. The key insight is that similarity means all corresponding sides scale by the same factor.

Intuitive explanation

This problem tests the SAS (Side-Angle-Side) similarity criterion: two triangles are similar if an included angle is equal and the sides forming that angle are proportional. Since ∠G=∠J\angle G = \angle J and you know all four sides around these angles, you need to set up the ratio of the sides at GG to the sides at JJ and use it to find the missing side. The key insight is that similarity means all corresponding sides scale by the same factor.

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