If triangle DEF has sides measuring 50, 40, and 32, is the triangle a right triangle? If it is a right triangle, answer with the number 90. If it is not a right triangle, answer with the number 0.(1 point
To find the length of the hypotenuse of a triangle, we can use the Pythagorean theorem, which states:
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.
Let's label the sides of the triangle:
- The longest side (opposite the right angle) as c (the hypotenuse)
- The other two sides as a and b
Using the Pythagorean theorem:
c² = a² + b²
Substituting the given lengths:
c² = 12² + 16²
c² = 144 + 256
c² = 400
To find the length of the hypotenuse c, we need to take the square root of both sides of the equation:
√(c²) = √400
c = 20
Therefore, the length of the hypotenuse is 20 units.
To determine if a triangle is a right triangle, we can use the Pythagorean theorem which states:
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.
If the given triangle has sides measuring 50, 40, and 32, we can find if it's a right triangle by checking if the Pythagorean theorem is satisfied.
Let's label the sides of the triangle:
- The longest side (opposite the right angle) as c (the hypotenuse)
- The other two sides as a and b
Using the Pythagorean theorem:
c² = a² + b²
Substituting the given lengths:
50² = 40² + 32²
2500 = 1600 + 1024
2500 = 2624
Since 2500 is not equal to 2624, the Pythagorean theorem is not satisfied in this case. Therefore, the triangle is not a right triangle.
The answer is: 0
If a triangle has sides of length 12 and 16 how long is the hypontenuse
To determine whether triangle DEF is a right triangle, we can use the Pythagorean theorem. According to the theorem, if a triangle is a right triangle, the sum of the squares of the lengths of the two shorter sides should be equal to the square of the length of the longest side.
Let's calculate:
The square of the length of the first side (50) is 50^2 = 2500.
The square of the length of the second side (40) is 40^2 = 1600.
The square of the length of the longest side (32) is 32^2 = 1024.
Now add the squares of the two shorter sides: 2500 + 1600 = 4100.
We can see that the sum of the squares of the two shorter sides (4100) is not equal to the square of the longest side (1024). Therefore, triangle DEF is not a right triangle.
So, the answer is 0.