find the perimeter and area of a right triangle if 1 leg measures 10 ft. and the other leg measures 24ft. show all work please.
a right triangle has to be 90 degrees right?
Right, so you can use Pythagorean theorem to find the hypotenuse.
10^2 + 24^2 = h^2
I'll let you do the rest of the work.
To find the perimeter and area of a right triangle, we need to use the formulae for each.
The perimeter of any polygon is simply the sum of the lengths of all its sides. In the case of a right triangle, the perimeter (P) is calculated by adding the lengths of the three sides. Let's call the two legs of the right triangle 'a' and 'b', and the hypotenuse 'c'.
In this problem, one leg measures 10 ft (a = 10ft) and the other leg measures 24 ft (b = 24ft).
Hence, the lengths of the three sides are:
a = 10 ft
b = 24 ft
c = hypotenuse (to be determined)
To calculate the hypotenuse (c), we can use the Pythagorean Theorem:
c^2 = a^2 + b^2
Plugging in the given values, we get:
c^2 = 10^2 + 24^2
c^2 = 100 + 576
c^2 = 676
c = √676
c = 26 ft
Now that we have all the side lengths, we can calculate the perimeter:
P = a + b + c
P = 10 ft + 24 ft + 26 ft
P = 60 ft
So, the perimeter of the right triangle is 60 ft.
For the area of a right triangle, we can use the formula:
Area (A) = (1/2) * base * height
Since this is a right triangle, we can choose either of the legs as the base and the other leg as the height. Let's choose the leg with length 10 ft as the base (b) and the leg with length 24 ft as the height (h).
A = (1/2) * 10 ft * 24 ft
A = 5 ft * 24 ft
A = 120 ft^2
Therefore, the area of the right triangle is 120 square feet.