A 45-45-90 triangle has a leg that is 5 cm long. Find the perimeter of the triangle to the nearest tenth
In a 45-45-90 triangle, the lengths of the legs are equal, so if one leg is 5 cm long, then the other leg is also 5 cm long.
Using the Pythagorean theorem, the length of the hypotenuse can be found:
c^2 = a^2 + b^2
c^2 = 5^2 + 5^2
c^2 = 25 + 25
c^2 = 50
Taking the square root of both sides, we find:
c = √50
c ≈ 7.07 cm
The perimeter of the triangle is the sum of the lengths of all its sides, so:
Perimeter = 5 cm + 5 cm + 7.07 cm
Perimeter ≈ 17.07 cm
Rounded to the nearest tenth, the perimeter of the triangle is approximately 17.1 cm.