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A park has 2 bike trails in the shape of similar quadrilaterals. Trail A has side lengths of 90m, 108m, 120m and 132m. The shortest side of Trail B is 45m. Luis rides his bike around Trail A once and Tara rides her bike around Trail B twice. Who rode the longest distance and by how much? Show all work for credit.
1 Answer
- 1 decade agoFavorite Answer
Since the quadrilaterals are similar, their sides are in ratio. (But by what ratio?)
You're given that the smallest side of B is 45m. The smallest side of A is 90m.
So you can see that any side A:B = 2:1.
Basically, the perimeter of A is twice of B.
(Alternatively, you could have found the lengths of all the sides of B by getting the matching side from A and dividing it by two, but this would have taken much longer)
Perimeter of A = 450m
Perimeter of B = 225m
The answer is that they both rode the same distance. A is twice the distance of B, but Tara rides around it twice.
Luis: 450 x 1
Tara: 225 x 2
They're the same, so they both rode 450m.