Question

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.

1. thugiang
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.