what is the perimeter of a right triangle with legs 6 cm and 3cm , leave the answer in simplest radical form
first we solve for hypotenuse:
to get the hypotenuse we use pythagorean theorem:
c^2 = a^2 + b^2
where
c = hypotenuse of the right triangle
a and b = legs of right triangle
substituting,
c^2 = 6^2 + 3^2
c^2 = 36 + 9
c^2 = 45
c = 3*sqrt(5)
therefore the perimieter is:
P = a + b + c
P = 6 + 3 + 3*sqrt(5)
P = 9 + 3*sqrt(5) cm
hope this helps~ :)
Math anwer
Why did the right triangle go to the comedy club?
Because it wanted to find its perimeter in a "simplest radical form" of humor!
But, let's not keep it waiting any longer. To find the perimeter of a triangle, you need to add up the lengths of all its sides. In this case, we have two legs measuring 6 cm and 3 cm.
So, the perimeter is equal to 6 cm + 3 cm + Hypotenuse.
Now, let me clown around with the Pythagorean theorem to find the hypotenuse. According to Pythagoras, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Using this marvelous formula, we get:
Hypotenuse^2 = 6^2 + 3^2
= 36 + 9
= 45
Now, let's simplify this radical party. The square root of 45 can be written as the square root of (9 x 5), and since 9 is a perfect square, we can take it out:
Hypotenuse = √(9 x 5)
= √9 x √5
= 3√5 cm
So, the perimeter of this right triangle, in its simplest radical form, is:
6 cm + 3 cm + 3√5 cm
And there you have it! The punchline is the perimeter: 9 + 3√5 cm. Have a great time exploring the triangle's perimeter!
To find the perimeter of a right triangle, we need to add the lengths of all three sides.
In a right triangle, the two shorter sides are called the legs, and the longest side is called the hypotenuse.
Given that the legs of the triangle are 6 cm and 3 cm, we can calculate the hypotenuse using 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 legs.
Using the Pythagorean theorem, we have:
Hypotenuse^2 = 6^2 + 3^2
Hypotenuse^2 = 36 + 9
Hypotenuse^2 = 45
To simplify the radical form, we can find the square root of 45:
√45 = √(9 * 5) = √9 * √5 = 3√5
Therefore, the length of the hypotenuse is 3√5 cm.
To find the perimeter, we add the lengths of the three sides:
Perimeter = 6 cm + 3 cm + 3√5 cm
Thus, the perimeter of the right triangle is 9 cm + 3√5 cm.
To find the perimeter of a triangle, you need to add the lengths of all its sides.
In a right triangle, the legs are the two sides that form the right angle. So, in this case, the legs of the right triangle are 6 cm and 3 cm.
To find the hypotenuse (the side opposite the right angle), 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 two legs.
The square of the leg 6 cm is 6^2 = 36.
The square of the leg 3 cm is 3^2 = 9.
Adding the squares of the legs, we get 36 + 9 = 45.
Now, we need to find the square root of 45 to get the length of the hypotenuse.
Since the square root of 45 cannot be simplified further, the length of the hypotenuse is √45 cm.
To find the perimeter, we add the lengths of all three sides:
Perimeter = 6 cm + 3 cm + √45 cm
So, the perimeter of the right triangle, leaving the answer in simplest radical form, is 9 cm + √45 cm.