A triangle has sides lengths 28 cm, and 53 cm. Is the triangle a right angle ?
To determine if the triangle is a right angle triangle, we need to determine if it satisfies the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) 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 side with length 28 cm is side a.
- The side with length 53 cm is side b.
- The hypotenuse is side c.
If the triangle is a right angle triangle, then a^2 + b^2 = c^2.
Let's calculate:
a^2 = 28^2 = 784 cm^2
b^2 = 53^2 = 2809 cm^2
If a^2 + b^2 = c^2, then c^2 = 784 + 2809 = 3593 cm^2.
Now, let's find the square root of 3593 to determine the length of side c: √3593 ≈ 59.92 cm.
Since c^2 ≈ 3593 cm^2 does not equal c^2 = 28^2 + 53^2 = 784 cm^2 + 2809 cm^2 = 3593 cm^2, the triangle is not a right angle triangle.
To determine whether the triangle is a right angle triangle, we can apply the Pythagorean Theorem. According to the theorem, in a right angle 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 denote the sides of the triangle as follows:
- The side with length 28 cm is denoted as a.
- The side with length 53 cm is denoted as b.
- The hypotenuse, which is the longest side, is denoted as c.
Using the Pythagorean Theorem, the equation becomes:
c^2 = a^2 + b^2
Substituting the given values, we have:
c^2 = 28^2 + 53^2
Calculating the squares of the lengths of the sides:
c^2 = 784 + 2809
c^2 = 3593
Now, we need to find the square root of 3593 to determine the length of the hypotenuse, c.
Taking the square root of both sides:
c = √3593
Using a calculator or approximation, we find the square root of 3593 is approximately 59.96.
So, the length of the hypotenuse, c, is approximately 59.96 cm.
Finally, we can conclude that this triangle is not a right angle triangle because the square of the hypotenuse is not equal to the sum of the squares of the other two sides.
To determine if a triangle is a right angle triangle, we can use the Pythagorean theorem. According to the Pythagorean theorem, in a right angle triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's calculate:
The shorter side has a length of 28 cm.
The longer side has a length of 53 cm.
To check if it's a right-angled triangle, we can use the equation:
a^2 + b^2 = c^2
where:
a = length of one side
b = length of the other side
c = length of the hypotenuse
Substituting the values:
28^2 + 53^2 = c^2
784 + 2809 = c^2
3663 = c^2
Taking the square root of both sides:
c = √3663
c ≈ 60.54
Since the square of the hypotenuse (60.54^2) is not equal to the sum of the squares of the other two sides (28^2 + 53^2), this triangle is not a right-angled triangle.