Sidney is traveling from the grocery store to the bank. There are two possible routes she can take, marked yellow and green in the diagram. Which statement is true?

Question

A simple map or diagram.

A gray square represents a city block.

The sides of the square are labeled with distances. The left side is labeled "4 miles" and the bottom side is labeled "3 miles".

Two dashed yellow lines form a right angle on the left and bottom sides of the block respectively.

A dashed green line diagonally connects the top left corner (labeled "Bank") to the bottom right corner (labeled "Grocery Store").

The labels "Bank", and "Grocery Store" are in blue text.

(1 point)
Responses

The green path is half the distance of the shorter path.
The green path is half the distance of the shorter path.

The green path is 2 miles shorter than the yellow path.
The green path is 2 miles shorter than the yellow path.

The yellow path is double the distance of the green path.
The yellow path is double the distance of the green path.

The yellow path and green path are the same distance.

Answer 1

To determine which statement is true regarding the distances of the yellow and green paths, we can calculate the lengths of each path based on the described routes.

1. Yellow Path: The yellow path forms a right angle using the dimensions of the block. Since the left side is 4 miles and the bottom side is 3 miles, we can find the total distance of the yellow path:

   • Length of left side (4 miles) + Length of bottom side (3 miles) = 4 miles + 3 miles = 7 miles.

2. Green Path: The green path is a diagonal line that connects the top left corner (Bank) to the bottom right corner (Grocery Store). To find the length of this diagonal path, we can use the Pythagorean theorem:

   • Distance = √(3 miles² + 4 miles²) = √(9 + 16) = √25 = 5 miles.

Now we can compare the distances:

• Yellow path: 7 miles
• Green path: 5 miles

Now let's evaluate the statements:

• The green path is half the distance of the shorter path. (False, since 5 is not half of 7)
• The green path is 2 miles shorter than the yellow path. (True, since 7 - 5 = 2)
• The yellow path is double the distance of the green path. (False, since 7 is not double 5)
• The yellow path and green path are the same distance. (False, since they are not equal)

Thus, the true statement is: The green path is 2 miles shorter than the yellow path.