Considering the Pythagorean theorem and the definition of perimeter, the perimeter of the triangle is 15.209 miles.
<h3>Right triangle</h3>
A right triangle is one that has an angle of 90º. The two sides that form the right angle are called legs, the opposite and longer side is called the hypotenuse.
<h3>Pythagorean theorem</h3>
The Pythagorean theorem is a mathematical premise that allows us to calculate the length of the sides of a right triangle.
The Pythagorean Theorem states the following:
<em>In any right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs</em>.
The Pythagorean theorem is only applicable to right triangles.
<h3>Definition of perimeter</h3>
The perimeter of a flat geometric figure is the length of its contour and is obtained as the result of the sum of the sides of a flat geometric figure.
<h3>Perimeter of a triangle</h3>
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. Knowing that:
Side a can be calculated by applying the Pythagorean theorem:
c²= a² + b²
Substituting the corresponding values:
6.3²= a² + 4.5²
Solving:
6.3²- 4.5²= a²
39.69 - 20.25= a²
19.44= a²
√19.44= a
<u><em>4.4090 miles= a</em></u>
On the other hand, the perimeter of the triangle is calculated by:
perimeter= a +b +c
Substituting the corresponding values:
perimeter= 4.4090 miles + 4.5 miles + 6.3 miles
Solving:
<u><em>perimeter= 15.209 miles</em></u>
Finally, the perimeter of the triangle is 15.209 miles.
Learn more about
the perimeter:
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brainly.com/question/660488
brainly.com/question/25092270
Pythagorean theorem:
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brainly.com/question/21691542
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