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?

A) 2x^2 - (x + 4) = (x^2 + 2)^2
B) 2x^2 + (x + 2) = (x + 4)
C) 2x^2 + (x + 2) = (x + 4)^2
D) 2x^2 + (x + 2) = x + 4

Answer 1

The correct equation that models the situation of a right triangle with sides represented by consecutive even integers is option C: 2x^2 + (x + 2) = (x + 4)^2, based on the application of the Pythagorean theorem.

Step-by-step explanation:

The student has asked which equation correctly models the situation where the sides of a right triangle are represented by three consecutive even integers, with x being the length of the shortest side. According to the Pythagorean theorem, the equation modeling the situation is a² + b² = c², where a and b are the lengths of the legs and c is the length of the hypotenuse.

In this case, if x is the shortest side, the other two sides would be x+2 and x+4, making x+4 the hypotenuse as it would be the longest side. Therefore, the equation is x² + (x+2)² = (x+4)², which simplifies to 2x² + 4x + 4 = x² + 8x + 16. Rewriting this gives us 2x² + 4x + 4 = (x+4)², which corresponds to option C: 2x² + (x + 2) = (x + 4)².