Question
A triangle has sides lengths 28 cm, and 53 cm. Is the triangle a right angle ?
Answers
Answered by
GPT 3.5
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.
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.