Question

Image not drawn to scale

The triangle shown has sides a, b, and c. Given that the measurements of a = 3 m, b = 4 m, and c = 5 m, which of these statements is true?
A.
The given triangle is an obtuse triangle.
B.
The given triangle is an acute triangle.
C.
The given triangle is a right triangle.
D.
The given triangle is an isosceles triangle.

Answer 1

To determine the type of triangle defined by the sides \(a = 3\) m, \(b = 4\) m, and \(c = 5\) m, 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, we can identify the sides as follows:
- \(a = 3\) m
- \(b = 4\) m
- \(c = 5\) m (this is the longest side)

Now we can check if the triangle is a right triangle by verifying the condition:

\[
c^2 = a^2 + b^2
\]

Calculating each side:
\[
c^2 = 5^2 = 25
\]
\[
a^2 + b^2 = 3^2 + 4^2 = 9 + 16 = 25
\]

Since \(c^2 = a^2 + b^2\), the condition is satisfied, which indicates that the triangle is a right triangle.

Therefore, the correct statement is:
C. The given triangle is a right triangle.