A park has 2 bike trails in the shape of similar quadrilaterals. Trail A has side lengths of 75m, 93m, 114m and 129m. The shortest side of Trail B is 100m. Luis rides his bike around Trail A twice and Tara rides her bike around Trail B once. Who rode the longest distance and by how much? Show all work for credit.

hey eaht are you learning in geometry? or are you all studing for the sol's?

In order to determine who rode the longest distance and by how much, we need to find the perimeter of each bike trail.

First, let's calculate the perimeter of Trail A. The perimeter of a quadrilateral is found by adding up the lengths of all its sides. So, for Trail A, we add up the given side lengths: 75m + 93m + 114m + 129m.

P(A) = 75m + 93m + 114m + 129m = 411m

Therefore, the perimeter of Trail A is 411m.

Now, let's calculate the perimeter of Trail B. We know that the shortest side of Trail B is 100m. However, we don't have information about the other side lengths, so we cannot calculate the exact perimeter.

Since we cannot determine the exact perimeter of Trail B, we cannot directly compare the distances ridden by Luis and Tara. To make a comparison, we can express the perimeter of Trail B in terms of the perimeter of Trail A.

The perimeter of Trail B must be greater than 411m, as the shortest side alone is 100m. So, assuming Trail B is also a quadrilateral, let's say its perimeter is P(B) = 411m + X, where X represents the additional distance to be added to 411m.

Now, we can compare the perimeters by considering the distance of each rider.

Luis rides around Trail A twice. Therefore, his total distance is 2 * P(A) = 2 * 411m = 822m.

Tara rides around Trail B once. So, her total distance is 1 * P(B) = 1 * (411m + X) = 411m + X.

Since we do not know the exact value of X, we cannot determine the difference in distances. We can only say that Luis rode a longer distance than Tara.

Therefore, Luis rode the longest distance, but we cannot determine by how much without additional information about the length of the other sides of Trail B.