Question

The sides of a right triangle are represented by three consecutive even integers. Let x be the length of the shortest side. Which of the following equations correctly models the situation?

Select one:

A) 2 + (x + 2) = x + 4

B) 2x + (x + 1)² = (2 + 2)

C) 2(x + 2)² = (x + 4)²

D) 2 + (x + 2) = (x + 4)²"

Answer 1

The correct equation that models a right triangle with sides of consecutive even integers is 2(x + 2)² = (x + 4)². This aligns with the Pythagorean theorem, which is a² + b² = c².

Step-by-step explanation:

The student is asking which equation models the situation where the sides of a right triangle are represented by three consecutive even integers, with x being the shortest side. According to the Pythagorean theorem, which states that a² + b² = c² for a right triangle with legs a and b, and hypotenuse c, we need to set up an equation that aligns with this relationship. In terms of x, the integer sides would be x, x+2, and x+4 (since they are consecutive even integers). Therefore, the correct equation modeling this situation would be x² + (x + 2)² = (x + 4)²

After squaring these values, the equation simplifies to:

x² + x² + 4x + 4 = x² + 8x + 16

Once we collect like terms and continue the simplification process, it becomes clear that the correct answer is option C: 2(x + 2)² = (x + 4)².