The length of the hypotenuse can be found using the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, let's denote the length of the hypotenuse as c. According to the Pythagorean theorem, we have 6^2 + 8^2 = c^2.
Simplifying the equation, we get 36 + 64 = c^2.
Combining like terms, we have 100 = c^2.
To find the length of the hypotenuse, we take the square root of both sides.
√100 = √c^2.
Taking the square root of 100 simplifies to 10, so c = 10.
Therefore, the length of the hypotenuse is 10.
If you have a right triangle with side lengths 6 and 8, what is the length of the hypotenuse? 1 point
12
7
10
8
7 answers
If the hypotenuse of a triangle is 13, and one side length is 5, what is the second side length? 1 point
7
10
12
8
7
10
12
8
To find the length of the second side in a right triangle with a hypotenuse of 13 and one side length of 5, you can use the Pythagorean theorem.
According to the theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's denote the length of the second side as b. Using the Pythagorean theorem, we have:
5^2 + b^2 = 13^2
Simplifying, we have:
25 + b^2 = 169
Subtracting 25 from both sides, we have:
b^2 = 144
Taking the square root of both sides, we have:
b = √144
Since 144 is a perfect square, the square root simplifies to 12.
Therefore, the second side length is 12.
According to the theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's denote the length of the second side as b. Using the Pythagorean theorem, we have:
5^2 + b^2 = 13^2
Simplifying, we have:
25 + b^2 = 169
Subtracting 25 from both sides, we have:
b^2 = 144
Taking the square root of both sides, we have:
b = √144
Since 144 is a perfect square, the square root simplifies to 12.
Therefore, the second side length is 12.
If the area of a square garden is 169 ft^2, what is the side length of the garden? * 1 point
14
18
13
12
14
18
13
12
The area of a square is calculated by squaring the length of its side. To find the side length of the garden, we need to take the square root of the area given.
Taking the square root of 169 gives us √169 = 13.
Therefore, the side length of the garden is 13.
Taking the square root of 169 gives us √169 = 13.
Therefore, the side length of the garden is 13.
Is the square root of 2 rational, or irrational? * 1 point
rational
irrational
rational
irrational
The square root of 2 is irrational.
1 answer