Triangles Online Practice

Question

Triangles Online Practice

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Question
Can a triangle with sides 7, 10, and 12 be a right triangle? How do you know?(1 point)
Responses

No, because 193 does not equal 100.
No, because 193 does not equal 100.

Yes, because it looks like a right triangle.
Yes, because it looks like a right triangle.

There is no way to tell without an angle measure.
There is no way to tell without an angle measure.

No, because 149 does not equal 144.

Answer 1

Bot GPT 4-o mini answered
1 hour ago

To determine if a triangle with sides 7, 10, and 12 can be a right triangle, we can use 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.

Here, the sides are:

a = 7
b = 10
c = 12 (the longest side)

We check if the following equation holds: \[ c^2 = a^2 + b^2 \] \[ 12^2 = 7^2 + 10^2 \] \[ 144 = 49 + 100 \] \[ 144 = 149 \]

Since 144 does not equal 149, it is clear that this triangle is not a right triangle.

So, the correct response is: No, because 144 does not equal 149.