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.

Answers

Considering the Pythagorean theorem and the definition of perimeter, the perimeter of the triangle is 15.209 miles.

Right triangle

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.

Pythagorean theorem

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:

In any right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

The Pythagorean theorem is only applicable to right triangles.

Definition of perimeter

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.

Perimeter of a triangle

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

4.4090 miles= a

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:

perimeter= 15.209 miles

Finally, the perimeter of the triangle is 15.209 miles.

perimeter of the triangleis15.209 miles.## Right triangle

angle of 90º. The two sides that form the right angle are calledlegs, the opposite and longer side is called thehypotenuse.## Pythagorean theorem

length of the sides of a right triangle.In any right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.only applicableto right triangles.## Definition of perimeter

length of its contourand is obtained as the result of the sum of the sides of a flat geometric figure.## Perimeter of a triangle

c²= a² + b²Substitutingthe corresponding values:4.4090 miles= aperimeter of the triangleis calculated by:perimeter= a +b +cSubstitutingthe corresponding values:perimeter= 15.209 milesperimeter of the triangleis15.209 miles.the perimeter:Pythagorean theorem: