OG详解-OG4 数学1 Q25

Choice C is correct. Since the triangle is an isosceles right triangle, the two sides that form the right angle must be the same length. Let x be the length, in inches, of each of those sides. The Pythagorean theorem states that in a right triangle, a² +b²  = c², where c is the length of the hypotenuse and a and b are the lengths of the other two sides. Substituting x  for a, x  for b, and 58 for c in this equation yields x² + x² = 582, or 2x² = 58² . Dividing each side of this equation by 2  yields x² =58​22 , or x² = 2·5824​.Taking the square root of each side of this equation yields two solutions: x = 58√22​​ and x = - 58√22​. The value of x must be positive because it represents a side length. Therefore,  x = 58√22, or  x = 29​√2. The perimeter, in inches, of the triangle is  58 + x + x , or  58 +2x. Substituting 29​√2 for x  in this expression gives a perimeter, in inches, of  58 +2(29​√2), or 58 +58​√2.
Choice A is incorrect. This is the length, in inches, of each of the congruent sides of the triangle, not the perimeter, in inches, of the triangle. Choice B is incorrect. This is the sum of the lengths, in inches, of the congruent sides of the triangle, not the perimeter, in inches, of the triangle. Choice D is incorrect and may result from conceptual or calculation errors.