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A triangle with sides of lengths 12 15 and 20 is a right triangle?
False. It can't be.In a right triangle, the sum of the squares of the two short sides is equal to the squareof the longest side.122 = 144152 = 225-------------sum = 369202 = 400, not 369.So these are not the sides of a right triangle.
In a right triangle the sum of the squares of the leg lengths is equal to the square of the hypotenuse length?
Correct.
Find the lengths of the side of the right triangle if the longest side of the triangle is four more than the shortest side and the middle side is two more than the shortest side?
There is no such right triangle. You have defined the relationship between three sides of a triangle that does not have a 90 degree angle. In a right triangle the sum of the squares of the shorter sides equals the square of the longest side and 12 + 22 = 5 ; 42 = 16 it does not equal 5 The angles in a triangle with sides 1, 2, 4 units can be found by applying the cosine rule.
What 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 legs?
the Pythagorean Theorem
This 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 legs?
pythagorean theorem.
If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides then the triangle is an acute triangle?
Yes, that's correct. In a triangle, if the square of the length of the longest side is less than the sum of the squares of the lengths of the other two sides, it indicates that all angles in the triangle are less than 90 degrees. This condition defines an acute triangle, where each angle is acute. Conversely, if the longest side squared equals the sum of the squares of the other two sides, the triangle is right-angled, and if it's greater, the triangle is obtuse.
What are the sides of a right angle triangle?
They are straight lines. The sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side. But subject to that constraint, the sides can have any lengths.They are straight lines. The sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side. But subject to that constraint, the sides can have any lengths.They are straight lines. The sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side. But subject to that constraint, the sides can have any lengths.They are straight lines. The sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side. But subject to that constraint, the sides can have any lengths.
Classify the triangle by its sides the lengths of the sides are 6 7 and 8?
The triangle with side lengths of 6, 7, and 8 is classified as a scalene triangle because all three sides have different lengths. Additionally, it is not a right triangle, as the square of the longest side (8) is not equal to the sum of the squares of the other two sides (6 and 7). Thus, it is simply a scalene triangle.
Which are the measurements of the sides of a right triangle?
There's an infinite list of 3-number sets that can be the lengths of the sides of aright triangle. The only fact that's true of all of them is:(square of the length of the longest side) = (sum of the squares of the lengths of the other two sides.)
In a right triangle the sum of the squares of the leg lengths is equal of the lengths is equal to the square of the hypotenuse?
Yes
True or false A triangle with sides of lengths 10 24 and 27 is a right triangle?
false In order for this to be a right triangle, the sum of the squares of the two shorter sides would have to equal the square of the longest side. 102=100 242= 576 272=729 102+242= 676, which does not equal 272=729, so a triangle with these lengths is not a right triangle.
Can you determine the type of a triangle by just knowing it's sides?
Yes. The three sides uniquely specify the triangle. If all three sides are equal it is equilateral. If only two are equal it is isosceles. If none are equal it is scalene. If the sum of the squares of the two shorter lengths is equal to the square of the longest length, it is a right angled triangle. If the sum of the squares on the two shorter sides is less than the square on the longest, it is an obtuse angled triangle. Otherwise it is an acute triangle.
Can 4m 5m 7m side lengths form a Right triangle?
To determine if the side lengths of 4m, 5m, and 7m can form a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the longest side (hypotenuse) equals the sum of the squares of the other two sides. Here, 7m is the longest side. Calculating, (4^2 + 5^2 = 16 + 25 = 41) and (7^2 = 49). Since (41 \neq 49), these side lengths cannot form a right triangle.
What is the length of a hypotenuse?
A hypotenuse is the longest side of a right angled triangle. The length of a hypotenuse can be found using the Pythagorean Theorem. This states that in a right angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. This means that to find the length of the hypotenuse, you need to know the lengths of the other two sides.
A triangle with sides of lengths 12 15 and 20 is a right triangle?
False. It can't be.In a right triangle, the sum of the squares of the two short sides is equal to the squareof the longest side.122 = 144152 = 225-------------sum = 369202 = 400, not 369.So these are not the sides of a right triangle.
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 legs?
Yes
In a right triangle the sum of the squares of the leg lengths is equal to the square of the hypotenuse length?
Correct.
