Find the perimeter and area of a right triangle if the shortest side is 16 in. and the longest side is 34 in. Include correct units with each part of your solution.
wow its been a long time
First, find the length of the third side by using the Pythagorean Theorem.
a^2 + b^2 = c^2
16^2 + b^2 = 34^2
256 + b^2 = 1,156
b^2 = 1,156 - 256
b^2 = 900
b = 30 inches
The perimeter is the length of all three sides added together.
The area is found with this formula:
A = bh/2
If you post your answers here, I'll check them for you.
the longest side in a right-angled triangle is the hypotenuse, let the missing side be x
x^2 + 16^2 = 34^2
x^2 = 900
x = 30
perimeter = sum of the three sides
area = (1/2)(16)(30) = ....
Should have checked first.
To find the perimeter and area of a right triangle, we need to know the lengths of two sides. In this case, we have the shortest side and the longest side given in inches. We can use the Pythagorean theorem to find the length of the third side.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's denote the shortest side as 'a', the longest side as 'b', and the third side as 'c' (the hypotenuse).
According to the Pythagorean theorem, we have:
a^2 + b^2 = c^2 .............. (1)
Given that the shortest side (a) is 16 in. and the longest side (b) is 34 in., we can substitute these values into equation (1):
(16)^2 + (34)^2 = c^2
256 + 1156 = c^2
1412 = c^2
To solve for 'c', we take the square root of both sides:
√1412 = √c^2
37.56 = c
So, the length of the third side 'c' (the hypotenuse) is approximately 37.56 inches.
Now that we have the lengths of all three sides, we can find the perimeter and area.
Perimeter:
The perimeter of a triangle is the sum of the lengths of all its sides. In this case, it will be the sum of the three sides:
Perimeter = a + b + c
Perimeter = 16 in + 34 in + 37.56 in
Perimeter = 87.56 in
Therefore, the perimeter of the triangle is approximately 87.56 inches.
Area:
The area of a right triangle can be calculated using the formula:
Area = (1/2) * base * height
In a right triangle, the base and height correspond to the two legs of the triangle (in this case, sides 'a' and 'b'). Given that 'a' is 16 in and 'b' is 34 in, we can substitute these values into the formula:
Area = (1/2) * 16 in * 34 in
Area = 272 in^2
Therefore, the area of the triangle is 272 square inches.