Question

the diagram shows the distance between your house, the bank, and the farmers market. you need to stop at the bank before going to the farmers market. given the information in the diagram, identify which statement is true.
(1 point)
the distance from your house to the bank and then the farmers market is equal to 5 miles.
the distance from your house to the bank and then the farmers market is greater than 5 miles.

Explanation:

Step1: Recall triangle - inequality theorem

In a triangle, the sum of the lengths of any two sides is greater than the length of the third side. Let the distance from the house to the bank be \(a = 5\) miles, the distance from the bank to the farmer's market be \(b\), and the distance from the house to the farmer's market be \(c\). Then \(a + b>c\).

Step2: Analyze the distance relationship

The distance from the house to the bank is 5 miles. The distance from the house to the farmer's market (going through the bank) is the sum of the distance from the house - to - bank and bank - to - market. Since the direct path (if possible) from the house to the market is shorter than the path through the bank (by the triangle - inequality theorem), the distance from the house to the bank and then to the farmer's market is greater than the direct distance from the house to the market. And the distance from the house to the bank is 5 miles. So the distance from the house to the bank and then to the farmer's market is greater than 5 miles.

Answer:

The distance from your house to the bank and then the farmer's market is greater than 5 miles.