Mathematics

Mathematics

Problem

In △GHI\triangle GHI and △JKL\triangle JKL, the side lengths are GH=4 cmGH = 4\text{ cm}, HI=5 cmHI = 5\text{ cm}, GI=6 cmGI = 6\text{ cm} and JK=6 cmJK = 6\text{ cm}, KL=7.5 cmKL = 7.5\text{ cm}, JL=9 cmJL = 9\text{ cm}. Which of the following is correct? a) The triangles are similar with scale factor 23\dfrac{2}{3} (from △GHI\triangle GHI to △JKL\triangle JKL). b) The triangles are not similar because the side ratios are unequal. c) The triangles are similar with scale factor 32\dfrac{3}{2} (from △GHI\triangle GHI to △JKL\triangle JKL). d) The triangles are congruent rather than similar.
Intuitive explanation

These two triangles are related by a scale factor—one is an enlarged version of the other. The key is to check if the ratios of corresponding sides are all equal. Line up the sides from smallest to largest in each triangle, then divide them: if you get the same ratio every time, the triangles are similar, and you've found your scale factor. This tells you which sides match up and how the triangles relate.

Intuitive explanation

These two triangles are related by a scale factor—one is an enlarged version of the other. The key is to check if the ratios of corresponding sides are all equal. Line up the sides from smallest to largest in each triangle, then divide them: if you get the same ratio every time, the triangles are similar, and you've found your scale factor. This tells you which sides match up and how the triangles relate.

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