Find the perimeter and area of a right triangle if the shortest side is 20 mm. and the longest side is 52 mm. Include correct units with each part of your solution.
To find the perimeter and area of a right triangle, you need to know the lengths of its sides. The given information states that the shortest side (which is also known as the base or the perpendicular side) is 20 mm, while the longest side (which is the hypotenuse) is 52 mm.
To find the other side of the right triangle (which is known as the height or the base side), you can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
Let's solve for the missing side (height or base side) using the Pythagorean theorem:
a² + b² = c²
where:
a = base side
b = height
c = hypotenuse
Substituting the given values, we have:
20² + b² = 52²
400 + b² = 2704
b² = 2704 - 400
b² = 2304
Taking the square root of both sides:
b = √2304
b = 48 mm
Now that we know the lengths of all three sides, we can proceed to find the perimeter and area of the right triangle.
Perimeter:
The perimeter of any polygon is the sum of the lengths of all its sides.
In this case, the perimeter of the right triangle is given by:
Perimeter = base + height + hypotenuse
Perimeter = 20 mm + 48 mm + 52 mm
Perimeter = 120 mm
Therefore, the perimeter of the right triangle is 120 mm.
Area:
The area of a right triangle can be calculated using the formula:
Area = (1/2) * base * height
In this case, the area of the right triangle is given by:
Area = (1/2) * 20 mm * 48 mm
Area = 480 mm²
Therefore, the area of the right triangle is 480 mm².