The missing diagram is shown below. Remember that shapes are similar if you can turn one into the other by moving, rotating, flipping, or scaling. So this means you can make the object bigger or smaller. So in this case, we know that ΔABC is similar to ΔDEF. If so, we can establish the following proportion:
Our goal is to find x. So by Pythagorean theorem:
Conclusion:
<em>ΔABC ~ΔDEF</em>
<em>Distance across the river is 25.34m </em>
<u><em>Answers:</em></u>
a. miles/day
b. 14 miles
<u><em>Explanation:</em></u>
<u>Part a:</u>
We are given that they paddled a total distance of 14 miles for 3 days. To get the distance paddled each day, we will divide the total paddled distance by the number of days
<u>This is done as follows:</u>
Distance paddled each day = miles/day
<u>Part b:</u>
<u>Now, we are given that:</u>
<u>i. They went half their daily distance:</u>
Daily distance = miles/day
<u>ii. They extended the trip twice as many days</u>
Number of days = 2 × 3 = 6 days
The total distance paddled will be equivalent to the product of the distance paddled each day and the total number of days
<u>This means that:</u>
Total distance = miles
Hope this helps :)
