Katrina lives directly east of the park. The football field is directly south of the park. The
library sits on the line formed between Katrina's home and the football field at the exact point
where an altitude to the right triangle formed by her home, the park, and the football field
could be drawn. The library is 4 miles from her home. The football field is 18 miles from the

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.

Here, mark the park as A, Home as B, Library as C and field as D.

Now, CD = 18 miles

BC = 4 miles

we have to find AC (distance between library and park)

BD = BC + CD = 18 + 4 = 22 miles

Using property of similar triangles,

AD² = BD X CD

AD² = 22 X 18

AD = √22 X √18

AD = 6√11 miles

By Pythagoras theorem,

AD² = AC² + CD²

396 = AC² + 324

AC² = 396 - 324

AC² = 72

AC = √72

AC = 6√2 miles

Thus, the distance between library and park is 6√2 miles and the distance between park and field is 6√11 miles.

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