How do I determine which of theses triangles are right triangles or not?
I am given a table with:
Traingle | Side 1| Side 2| Side 3|
Q |6 6 30
R |6 4 10
S |5 4 41
T |5 4 3
I Know the equation a^2+b^2=c^2, and have applied it to this, but cannot get an answer…Help me please.
try to understand the answers here. jiskha dot com/display.cgi?id=1354313665
(remove the spaces, change dot into an actual dot ( . ))
To determine whether a triangle is a right triangle or not, you can indeed use the Pythagorean theorem, which 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, you are given the lengths of the three sides of each triangle. To determine if a triangle is a right triangle, follow these steps for each triangle:
1. Calculate the squares of the lengths of the sides.
2. Identify the two shorter side lengths. Let's call them a and b.
3. Identify the longest side length. Let's call it c.
4. Plug in the values of a, b, and c into the Pythagorean theorem equation, a^2 + b^2 = c^2.
5. Check if the equation is satisfied.
Let's apply these steps to the triangles given in your table:
For Triangle Q:
Side 1 = 6, Side 2 = 6, Side 3 = 30
Calculating the squares of the side lengths: 6^2 = 36, 6^2 = 36, 30^2 = 900
Identifying the two shorter sides: a = 6, b = 6
Identifying the longest side: c = 30
Applying the Pythagorean theorem: 6^2 + 6^2 = 36 + 36 = 72 ≠ 30^2 = 900
Since the equation is not satisfied, Triangle Q is not a right triangle.
For Triangle R:
Side 1 = 6, Side 2 = 4, Side 3 = 10
Calculating the squares of the side lengths: 6^2 = 36, 4^2 = 16, 10^2 = 100
Identifying the two shorter sides: a = 4, b = 6
Identifying the longest side: c = 10
Applying the Pythagorean theorem: 4^2 + 6^2 = 16 + 36 = 52 ≠ 10^2 = 100
Since the equation is not satisfied, Triangle R is not a right triangle.
For Triangle S:
Side 1 = 5, Side 2 = 4, Side 3 = 41
Calculating the squares of the side lengths: 5^2 = 25, 4^2 = 16, 41^2 = 1681
Identifying the two shorter sides: a = 4, b = 5
Identifying the longest side: c = 41
Applying the Pythagorean theorem: 4^2 + 5^2 = 16 + 25 = 41 = 41^2
The equation is satisfied, so Triangle S is a right triangle.
For Triangle T:
Side 1 = 5, Side 2 = 4, Side 3 = 3
Calculating the squares of the side lengths: 5^2 = 25, 4^2 = 16, 3^2 = 9
Identifying the two shorter sides: a = 3, b = 4
Identifying the longest side: c = 5
Applying the Pythagorean theorem: 3^2 + 4^2 = 9 + 16 = 25 = 5^2
The equation is satisfied, so Triangle T is a right triangle.
Therefore, out of the given triangles, only Triangle S and Triangle T are right triangles.