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Leokris [45]
2 years ago
9

In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If b=4.5 miles and c=6.3 miles,

what is the perimeter? If necessary, round to the nearest tenth.
Mathematics
1 answer:
Alina [70]2 years ago
8 0

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:

  • b=4.5 miles.
  • c=6.3 miles.

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:

brainly.com/question/15267339

brainly.com/question/660488

brainly.com/question/25092270

Pythagorean theorem:

brainly.com/question/654982

brainly.com/question/21691542

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