The area ratio between 2 similar triangles is 225/81. Find the perimeter ratio of these triangles.
a) 3/2
b) 225/81
c) 15/9
The areas of two similar figures are proportional to the square of their corresponding sides
so 225 : 81 = side1^2 : side2^2
then √225 : √81 = side1 : side2
side1 : side2 = 15 : 8
you mean 15 : 9?
yes, of course, hit the wrong key
how do I find the square root of the area ratio?
To find the perimeter ratio of two similar triangles given their area ratio, we need to find the square root of the area ratio. The square root of the area ratio will give us the ratio of their corresponding side lengths, which is then used to find the perimeter ratio.
Given that the area ratio is 225/81, we can find the square root of this ratio:
√(225/81) = √(225)/√(81) = 15/9
Therefore, the ratio of their side lengths is 15/9.
To find the perimeter ratio, we need to add up the corresponding side lengths of each triangle in the ratio and then compare those sums.
The perimeter ratio is given by:
Perimeter ratio = (Sum of side lengths of the first triangle) / (Sum of side lengths of the second triangle)
Let's assume the sum of the side lengths of the first triangle is 15x and the sum of the side lengths of the second triangle is 9x.
Therefore, the perimeter ratio is:
Perimeter ratio = (15x) / (9x) = 15/9
Thus, the correct answer is c) 15/9.