a 45-45-90 triangle has a leg that is 5cm long. find the perimeter of the triangle to the nearest tenth
In a 45-45-90 triangle, the two legs are congruent, meaning they have the same length. Therefore, if one leg of the triangle is 5 cm long, then the other leg is also 5 cm long.
The ratio of the sides in a 45-45-90 triangle is 1:1:√2. This means that the hypotenuse is √2 times the length of the legs.
The length of the hypotenuse is √2 * (5 cm) ≈ 7.1 cm.
The perimeter of the triangle is the sum of the lengths of all three sides, which is 5 cm + 5 cm + 7.1 cm = 17.1 cm.
Rounded to the nearest tenth, the perimeter of the triangle is 17.1 cm.