Find the length of the top of the awning and add 6 inches to it.
At most 7.5 ft
Practice makes perfect
Let's call the length of the top of the awning x ft. To find its value we need to consider the given triangle.
By the Triangle Inequality Theorem, the sum of the length of any two sides of a triangle must be less than the length of the third side. Using this theorem, we can form three inequalities.
3+4>x
3+x>4
4+x>3
Let's solve them by isolating x on one side of each inequality.
Inequality
Solution Set
3+4>x
7>x
3+x>4
x>1
4+x>3
x>- 1
We can find the common solutions by graphing these inequalities.
All three lines overlap on the segments from 1 to 7. Therefore, the length of the top of the awning is between 1 and 7 feet. We are also told that 6 inches or 0.5 ft of the material will drape over the front. Adding this value to the maximum length of 7 ft, we can calculate the total length of the material.
7+0.5=7.5ft
Therefore, Carlota should buy at most 7.5 ft.
