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

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(648) (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
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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

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