Questions: triangle has sides with lengths of 4 meters, 5 meters, and 7 meters. Is it a right triangle?

Solution Steps

To determine if a triangle with sides of lengths 4 meters, 5 meters, and 7 meters is a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) should be equal to the sum of the squares of the other two sides. We will check if \(7^2 = 4^2 + 5^2\).

The lengths of the sides of the triangle are given as \( a = 4 \) meters, \( b = 5 \) meters, and \( c = 7 \) meters. Here, \( c \) is the longest side.

To determine if the triangle is a right triangle, we apply the Pythagorean theorem, which states that for a right triangle:

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

Substituting the values:

\[ 7^2 = 4^2 + 5^2 \]

Calculating each side:

\[ 49 \neq 16 + 25 \]

This simplifies to:

\[ 49 \neq 41 \]

Since \( 49 \) is not equal to \( 41 \), the triangle with sides of lengths \( 4 \), \( 5 \), and \( 7 \) meters is not a right triangle.

Final Answer