FIND THE PERIMETER AND AREA OF A RIGHT IF THE SHORTEST SIDE IS 20MM. AND THE LONGEST SIDE IS 52MM. INCLUDE CORRECT UNITS WITH EACH PART OF YOUR SOLUTION.
Is this a right TRIANGLE?
If it is, I'll be glad to help you.
YES
First, we need to determine the length of the third side by using the Pythagorean Theorem.
a^2 + b^2 = c^2
20^2 + b^2 = 52^2
400 + b^2 = 2704
b^2 = 2304
b = 48
The perimeter is the sum of the three sides.
20 + 48 + 52 = P
The area is found by using this formula:
A = 1/2 * b * h
A = (1/2) * 20 * 48
A = ________sq. mm.
To find the perimeter and area of a right triangle, we need to know the lengths of its sides. In this case, we have the shortest side as 20 mm and the longest side as 52 mm.
Let's start by determining the missing side length. In a right triangle, the longest side is called the hypotenuse, and it is related to the other two sides (the legs) by the Pythagorean theorem:
a^2 + b^2 = c^2
where:
a and b are the lengths of the legs
c is the length of the hypotenuse
In our case, one leg is 20 mm and the hypotenuse is 52 mm. Let's solve for the missing leg, which we'll call "a":
a^2 + 20^2 = 52^2
a^2 + 400 = 2704
a^2 = 2304
Taking the square root of both sides, we find:
a = √2304
a = 48 mm
So, the missing leg has a length of 48 mm.
Now, we can proceed to find the perimeter and area.
1. Perimeter:
The perimeter of any shape is the sum of the lengths of all its sides. In a triangle, the perimeter is found by adding up the lengths of all three sides.
Given that the lengths of the three sides are 20 mm, 48 mm, and 52 mm, we can find the perimeter:
Perimeter = 20 mm + 48 mm + 52 mm
Perimeter = 120 mm
Therefore, the perimeter of the right triangle is 120 mm.
2. Area:
The area of a right triangle can be calculated by multiplying the lengths of the two legs and dividing by 2.
Given that the lengths of the legs are 20 mm and 48 mm, we can find the area:
Area = (20 mm x 48 mm) / 2
Area = 480 mm^2
Therefore, the area of the right triangle is 480 mm^2.
In summary, the perimeter of the right triangle is 120 mm, and the area is 480 mm^2.