A triangle with sides of lengths 16, 30, and 35 is a right triangle.A.TrueB.False

To determine whether the triangle with sides of lengths 16, 30, and 35 is a right triangle, we can use the Pythagorean theorem. The theorem states that for 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.

1. ### Break Down the Problem

• Identify the sides of the triangle: $a = 16$, $b = 30$, $c = 35$ (hypotenuse).
• We need to check if $c^2 = a^2 + b^2$.

2. ### Relevant Concepts

• Pythagorean theorem: $c^2 = a^2 + b^2$

3. ### Analysis and Detail

• Calculate $c^2$: $c^2 = 35^2 = 1225$
• Calculate $a^2 + b^2$: $a^2 = 16^2 = 256$ $b^2 = 30^2 = 900$ $a^2 + b^2 = 256 + 900 = 1156$

4. ### Verify and Summarize

• Compare $c^2$ and $a^2 + b^2$: $c^2 = 1225 \quad \text{and} \quad a^2 + b^2 = 1156$ Since $1225 \neq 1156$, the triangle is not a right triangle.

Final Answer

B. False