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 in solution.
Now I did one very similar to this for you a couple of hours ago. You try.
i think P = a + b + c right?
and A = 1/2bh right?
yes and c = 52 = sqrt (a^2+b^2)
(because the longest side is the hypotenuse, not one of the legs)
im still a little confused with this problem....
i don't think im getting this problem...would it be 20 * 52 = 1040 mm?
PLEASE ASSIST :(
To find the perimeter and area of a right triangle, you'll need to use the lengths of its sides. In this case, you're given that the shortest side (called the base) is 20 mm and the longest side (called the hypotenuse) is 52 mm.
To find the remaining side (called the height), you can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Applying the Pythagorean theorem:
c^2 = a^2 + b^2
Where:
c is the length of the hypotenuse (52 mm)
a is the length of the shortest side (20 mm)
b is the length of the height (which we need to find)
Solving for b:
b^2 = c^2 - a^2
b^2 = 52^2 - 20^2
b^2 = 2704 - 400
b^2 = 2304
b = sqrt(2304)
b = 48 mm
Now that we know the lengths of all three sides, we can find the perimeter and area of the triangle.
Perimeter:
The perimeter is the sum of all the side lengths. In this case, we have the base (20 mm), the hypotenuse (52 mm), and the height (48 mm).
Perimeter = base + hypotenuse + height
Perimeter = 20 mm + 52 mm + 48 mm
Perimeter = 120 mm
So, the perimeter of the right triangle is 120 mm.
Area:
The area of a right triangle can be calculated using the formula: Area = (base * height) / 2
Area = (20 mm * 48 mm) / 2
Area = 960 mm² / 2
Area = 480 mm²
Therefore, the area of the right triangle is 480 mm².