Video: Finding the Perimeter of a Triangle given the Perimeter of a Similar Triangle and a Ratio between Their Areas

The ratio of the areas of two similar triangles is 9/100. If the perimeter of the larger triangle is 129, what is the perimeter of the smaller one?

02:20

Video Transcript

The ratio of the areas of two similar triangles is nine 100th. If the perimeter of the larger triangle is 129, what is the perimeter of the smaller one?

Notice that we’re given the ratio of the areas. But we’re asked to solve for a perimeter. That means we do not want to use the ratio of an area. We want to use the ratio of a perimeter. The relationship between an area ratio and a perimeter ratio is that an area ratio is equal to a perimeter ratio squared.

Essentially, the ratio of the areas of the surfaces of two similar triangles equals the square of the ratio of the length of any two corresponding sides of the triangle. And since the ratio of the area of two similar triangles we know to be equal to nine 100th, let’s go ahead and plug that in for the area ratio. So here, we’ve done that.

And as we said before, the ratio of the areas of the surfaces of two similar triangles equals the square of the ratios of the lengths. Well, a perimeter is a length. So what we have is perfect. So in order to solve for a perimeter ratio, we need to square root both sides of the equation. So we need to take the square root of nine and the square root of 100. The square root of nine is three and the square root of 100 is 10.

So now, let’s use this perimeter ratio to solve for the perimeter of the smaller triangle. So out of three 10ths, three is the smaller number. So it needs to be across from the smaller perimeter. And since 10 is the larger number, it should be across from the larger perimeter. And we actually know the perimeter of the larger triangle. So we will plug in 129 for the larger triangle perimeter.

And so to solve for the smaller perimeter, we need to cross multiply and solve. So we take three times 129 and set it equal to the smaller perimeter times 10. So three times 129 is equal to 387. Now, we need to divide both sides by 10, resulting in 38.7 will be the perimeter of the smaller triangle.

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