# SOLUTION: triangle ABC has sides of lengths of 12, 15 and 17. The smallest side of a similar triangle has length 5. What is the perimeter of the similar triangle? The area of the larger t

Algebra ->  Algebra  -> Triangles -> SOLUTION: triangle ABC has sides of lengths of 12, 15 and 17. The smallest side of a similar triangle has length 5. What is the perimeter of the similar triangle? The area of the larger t      Log On

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 Geometry: Triangles Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Triangles Question 609328: triangle ABC has sides of lengths of 12, 15 and 17. The smallest side of a similar triangle has length 5. What is the perimeter of the similar triangle? The area of the larger triangle is __________ times the area of the smaller triangle. 12+15+17=44 12-5 5+8+10 Thanks for the help!Answer by math-vortex(472)   (Show Source): You can put this solution on YOUR website!Hi, there-- . The triangles are similar, so their corresponding sides are proportional. Similar triangles have the same shape, but differ by some scale factor (like enlarging or shrinking on a copier). The key to solving problems with similar figures is to set up proportions between corresponding sides. . The shortest side on the small triangle corresponds to the side of triangle ABC with length 12 since it is the shortest side. We can set up a ratio to find the scale factor--12:5, or 2.4:1. The scale factor from the small triangle to the larger is 2.4. . I. PERIMETER Let's have P be the perimeter of the smaller triangle. The perimeters of the two triangles will differ by the same scale factor. To find the perimeter, we write a proportion. . . . . II. AREA Area is a bit different. The area of similar figures differ by the SQUARE of the scale factor. There is a nice explanation about why this is the case at this link. (Scroll down to #3.) . http://www.mathsisfun.com/geometry/triangles-similar-theorems.html . In this case, the square of 2.4 is 5.76. The area of the large triangle is 5.76 times the area of the small triangle. . Hope this helps. Feel free to email if you have questions. . Ms.Figgy math.in.the.vortex@gmail.com