Answer :
function that could be used to represent the area of the triangular region formed by the girls' locations and the campsite at 2:30 p.m. is [tex]Area = \frac{(2x+1)(x+0.5)}{2}[/tex] .
Step-by-step explanation:
First, Kara walks straight East twice as much as Lindsay walks North. Let "x" be the number of miles walked by Lindsay, Kara has walked twice that at the same time i.e.
⇒ [tex]2x[/tex]
Then we need to add one mile to what Kara walked i.e.
⇒ [tex]2x+1[/tex] and half a mile (0.5 mi) to what Lindsey walked i.e.
⇒ [tex]x+0.5[/tex] . We represent the distances covered East and North from the campsite in the following sketch: Distances covered are straight & are in right triangle !
Area of triangle = [tex]\frac{1}{2}base(height)[/tex]
⇒ [tex]Area = \frac{1}{2}base(height)[/tex]
⇒ [tex]Area = \frac{1}{2}(2x+1)(x+0.5)[/tex]
⇒ [tex]Area = \frac{(2x+1)(x+0.5)}{2}[/tex]
Therefore , function that could be used to represent the area of the triangular region formed by the girls' locations and the campsite at 2:30 p.m. is [tex]Area = \frac{(2x+1)(x+0.5)}{2}[/tex] .
