Find the perimeter and area of a right triangle if one leg measures 24ft and the other leg measures 70ft. Shoe step by step please.
First, find the hypotenuse (c) using the Pythagorean theorem.
24^2 + 70^2 = c^2
Add these three measurements for the perimeter.
For the area, use this formula:
A = 1/2 * b * h
We'll be glad to check your answers.
840
To find the perimeter and area of a right triangle with given leg lengths, follow these step-by-step instructions:
1. Identify the given information: In this case, one leg measures 24 ft and the other leg measures 70 ft.
2. Find the hypotenuse: The hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. The formula is: c^2 = a^2 + b^2, where c represents the hypotenuse and a and b represent the legs. Applying this formula: c^2 = 24^2 + 70^2.
Simplifying the equation: c^2 = 576 + 4900.
c^2 = 5476.
Taking the square root of both sides: c ≈ 73.975.
Therefore, the hypotenuse measures approximately 73.975 ft.
3. Find the perimeter: The perimeter of a triangle is the sum of all three sides. For our triangle, the perimeter is the sum of the two legs and the hypotenuse. Adding the given lengths: Perimeter = 24 + 70 + 73.975.
Simplifying: Perimeter ≈ 167.975 ft.
Therefore, the perimeter of the triangle is approximately 167.975 ft.
4. Find the area: The area of a right triangle can be calculated using the formula: Area = (base * height) / 2. In our case, we can choose either leg as the base and the other as the height. Let's choose the leg of 24 ft as the base and the leg of 70 ft as the height. Applying the formula: Area = (24 * 70) / 2.
Simplifying: Area = 1680 / 2.
Area = 840 sq ft.
Therefore, the area of the triangle is 840 square feet.
In summary, the perimeter of the right triangle is approximately 167.975 ft, and the area is 840 sq ft.