Find the perimeter and area of a right triangle if the shortest side is 20 mm. and the longest side is 52 mm.
See later post.
The shortest side, we are told, is 20mm. This is one of the 'legs' of the right triangle, adjacent to the right angle.
We are told that the longest side is 52mm. This by definition is the hypotenuse (the side OPPOSITE the right angle). Hence the side we are trying to find the length of is the other 'leg' which has intermediate value.
Using Pythagoras' Theorem, and allowing the unknown 'base/ leg' be x:
(20)^2 + (x)^2 = (52)^2
or (4000 + (x^2) = (2704)
implying x = 48mm after simplification, etc..
The Perimeter, therefore, is (20+48+52)mm = 120mm.
The area , therefore, is = 1/2 * base * perp. height
Area = 1/2 * 48 * 20 = 480 mm^2.
To find the perimeter and area of a right triangle, we need to know the lengths of at least two sides. In this case, we have the lengths of the shortest side (20 mm) and the longest side (52 mm). Since the longest side of the triangle is the hypotenuse in a right triangle, 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 is equal to the sum of the squares of the lengths of the other two sides.
Let's label the unknown side length as 'a'. Using the Pythagorean theorem, we can write the equation as:
a^2 = 52^2 - 20^2
Calculating this equation will give us the value of 'a'.
a^2 = 2704 - 400
a^2 = 2304
Taking the square root of both sides:
a = √2304
a ≈ 48
So, the length of the third side (a) is approximately 48 mm.
Now that we have all three side lengths, we can calculate the perimeter and area of the right triangle:
Perimeter of a triangle = sum of all side lengths
P = 20 + 52 + 48
P = 120 mm
Therefore, the perimeter of the right triangle is 120 mm.
To find the area of a right triangle, we can use the formula:
Area of a triangle = (base * height) / 2
Since we have a right triangle, the base can be any of the two shorter sides. Let's take the shortest side (20 mm) as the base, and the third side (48 mm) as the height. Plugging in the values into the formula:
Area = (20 * 48) / 2
Area = 960 / 2
Area = 480 square mm
Hence, the area of the right triangle is 480 square mm.