Question

Kara and Lindsey both hike in separate directions from their campsite, with Kara hiking straight to the east and Lindsey hiking straight north. At 2:00 p.m., Kara hiked twice as far to the east as Lindsey hiked to the north. At 2:30 p.m., Kara had covered another mile, while Lindsey had covered another half of a mile. If x represents Lindsey's distance, in miles, from the campsite at 2:00 p.m., what function could be used to represent the area of the triangular region formed by the girls' locations and the campsite at 2:30 p.m.?

Answer 1

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 $Area = \frac{(2x+1)(x+0.5)}{2}$ .

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.

⇒ $2x$

Then we need to add one mile to what Kara walked i.e.

⇒ $2x+1$  and half a mile (0.5 mi) to what Lindsey walked i.e.

⇒ $x+0.5$  . 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 = $\frac{1}{2}base(height)$

⇒ $Area = \frac{1}{2}base(height)$

⇒ $Area = \frac{1}{2}(2x+1)(x+0.5)$

⇒ $Area = \frac{(2x+1)(x+0.5)}{2}$

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 $Area = \frac{(2x+1)(x+0.5)}{2}$ .