Find the perimeter and area of a right triangle if the shortest side is 20 mm. and the longest side is 52 mm.
The longest side of a right triangle is the hypotenuse, c in
a^2 + b^2 = c^2
so
a^2 + 20^2 = 52^2
a^2 = 2704 - 400 = 2304
a = 48
perimeter = 48 + 20 + 52 = 120 mm
area = (1/2)48(20) = 480 mm^2
oh thank you so much!! i was totally off...
You are welcome :)
To find the perimeter of a triangle, you need to add up the lengths of all its sides. In this case, we have a right triangle with three sides: the shortest side (20 mm), the longest side (52 mm), and the hypotenuse (the side opposite the right angle).
To find the hypotenuse in a right triangle, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
So, in this case, we have:
hypotenuse^2 = shortest side^2 + longest side^2
hypotenuse^2 = 20^2 + 52^2
hypotenuse^2 = 400 + 2704
hypotenuse^2 = 3104
To find the hypotenuse, we need to take the square root of both sides:
hypotenuse = √3104
hypotenuse ≈ 55.68 mm
Now that we know the lengths of all three sides, we can calculate the perimeter by adding them together:
perimeter = shortest side + longest side + hypotenuse
perimeter = 20 + 52 + 55.68
perimeter ≈ 127.68 mm
To find the area of a right triangle, you can use the formula:
area = 1/2 * base * height
In a right triangle, the shortest side and the longest side are the base and height, respectively (or vice versa).
So, in this case, the area would be:
area = 1/2 * shortest side * longest side
area = 1/2 * 20 * 52
area = 520 mm²
Therefore, the perimeter of the right triangle is approximately 127.68 mm, and its area is 520 mm².