MGMAT Strategy Guide: Geometry - Triangles Problem Set # 7

[fang6]

2 Similar Triangles have areas in the ratio 9:1. What is the ratio of the triangles perimeters ?

I understand the resolution up to the point where X = 3. However I don't understand how once we have X = 3, one can jump to the conclusion that the "ratio of the linear measurements (perimeter)" is 3:1 I am missing something here. I don't understand how from X=3 we derive the ratio for the linear measurements.

Thanks if someone can explain.

[rfernandez]

In the solution, the smaller triangle has base b and height h. The larger (similar) triangle is described as having base bx and height hx. By definition, therefore, x is the ratio of the triangles' linear measurements. In other words, corresponding linear measurements are related by a x:1 ratio. That includes the triangles sides and perimeters. So solving for x is all you need to answer the question.

I hope this clarifies it.

[fang6]

Hi Rey - Many thanks for posting this reply it clarifies everything ! Thank you

[StaceyKoprince]

Glad Rey could help you out!