Question

Stephen is making a map of his neighborhood. He knows the following information: The distance from his home to the park is 10 blocks The distance from his home to his friend's house is 15 blocks The distance from the grocery store to his home is 9 blocks A street map is shown. The streets form a triangle comprised of the locations of home, friends house, and the grocery store. The triangle is intersected by a line formed by the park and the bus stop. Stephen wants to use the Side-Angle-Side Similarity Theorem to determine the triangles are similar. Which other distance does he need to know? The distance from the bus stop to the grocery store is 3 blocks The distance from the bus stop to his home is 6 blocks The distance from the grocery store to his friend's house is 8 blocks The distance from the park to his friend's house is 5 blocks

Answer 1

I think it my be "The distance from the bus stop to his home is 6 blocks"
But im not sure I may be wrong.

Answer 2

Answer : The distance from the bus stop to his home is 6 blocks

The graph of the given information is attached below

The distance from his home to the park =10 blocks

The distance from his home to his friend's house = 15 blocks

The distance from the grocery store to his home = 9 blocks

By Side-Angle-Side Similarity , the sides are in proportions

So we make a proportion using the similar triangles

`(distance \ from \ home \ to \ the \ friend's \ house)/(distance \ from \ home \ to \ the \ park) = (distance \ from \ home \ to \ the \ grocery)/(distance \ from \ home \ to \ the \ bus stop)`

`(15)/(10) = (9)/(x)`

15x = 90 ( Divide by 15 on both sides)

x= 6 blocks

The distance from the bus stop to his home is 6 blocks