We want to find the area of the region the zookeeper needs to search. Let's look at the diagram!
The given region is a triangle. This means that we can use the formula for the area of a triangle.
A= 12bh
In the formula for the area of a triangle, b is the base and h is the height of the triangle. The height of a triangle must be perpendicular to the base. Because our triangle is a right triangle, we can choose either one of the legs to be the height. Let's identify b and h on the diagram.
We can see that b is 2.4 miles and h is x miles.
A= 12 b h ⇒ A= 12( 2.4)( x)
In this case, we need to start by finding x. To do so, we can use the Pythagorean Theorem.
Pythagorean Theorem
In any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
By the Pythagorean Theorem, the following equation is true.
a^2+b^2=c^2
In the formula, a and b are the legs of a triangle and c is the hypotenuse of a triangle. We know that legs of our triangle measure x miles and 2.4 miles. The length of the hypotenuse is 7.4 miles. Let's substitute these values into the Pythagorean Theorem.
x^2+( 2.4)^2=(7.4)^2
We can solve this equation for x.
We found that x is 7. Finally, we can substitute 7 for x in the formula for the area of the triangle.
A= 12( 2.4)( x) ⇒ A= 12( 2.4)( 7)
Let's calculate the area of the triangular region!
