According to the diagram, there are two ways to get from Larry's house to his grandmother's house.
Travel Route
Distance (blocks)
Main Street
5
Exchange Street and Market Street
d+3
We want to calculate the distance saved if Larry takes Main Street instead of Market and Exchange. To do so, we need to find the value of d. Let's start by taking a closer look at the diagram.
Notice that the stretch of Exchange Street with a length of d blocks is also a leg of a right triangle. This means that we can use the Pythagorean Theorem to find the missing length.
a^2+ b^2= c^2
In the formula, a and b are the lengths of the legs and c is the length of the hypotenuse of a right triangle. We are given a triangle with a= 3, b= d, and c= 5.
Let's substitute these values into the formula.
a^2+ b^2= c^2
⇕
3^2+ d^2= 5^2
Now we can solve the equation that we got to find the value of d.
Since a negative side length does not make sense, we only need to consider positive solutions. Therefore, this stretch of Exchange Street is 4 blocks long. Now we can compare the distances!
Travel Route
Distance (blocks)
Main Street
5
Exchange Street and Market Street
4+3=7
Let's calculate the difference between these distances.
7-5=2
Therefore, if Larry takes Main Street instead of Market and Exchange, the trip will be two blocks shorter.
