Questions: The following side lengths of a triangle form a right triangle. 4,5.6,7.07 When checking your numbers, round all your numbers to the nearest integer. True False

Solution Steps

To determine if the given side lengths form 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 round the side lengths to the nearest integer and then check if the condition holds.

The given side lengths are \( a = 4 \), \( b = 5.6 \), and \( c = 7.07 \). Rounding these to the nearest integer gives:

• \( a_{\text{rounded}} = 4 \)
• \( b_{\text{rounded}} = 6 \)
• \( c_{\text{rounded}} = 7 \)

To check if these sides form a right triangle, we first sort the rounded lengths:

• Sorted sides: \( [4, 6, 7] \) Here, the longest side \( c_{\text{rounded}} = 7 \) is considered the hypotenuse.

According to the Pythagorean theorem, for a right triangle, the following must hold: \[ a^2 + b^2 = c^2 \] Substituting the rounded values: \[ 4^2 + 6^2 = 7^2 \] Calculating each side: \[ 16 + 36 = 49 \] This simplifies to: \[ 52 \neq 49 \] Thus, the condition does not hold.

Final Answer