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- - - -_an_equilateral_triangle_is - - - - - ~ The perimeter of 624 centimeters. The height of this triangle is k 3 centimeters, where k is a constant. What is the value of k? OP
Correct answer: 104 (parsed from the explanation — this source omits an answer key for this item)
Explanation
104 The correct answer is . An equilateral triangle is a triangle in which all three 60° sides have the same length and all three angles have a measure of . The height of the triangle, k 3, is the length of the altitude from one vertex. The altitude divides the equilateral triangle into two congruent 30-60-90 right triangles, where 60° the altitude is the side across from the angle in each 30-60-90 right triangle. Since the altitude has a length of k 3, it follows from the properties of 30° 30-60-90 right triangles that the side across from each angle has a length of k and each hypotenuse has a length of 2k. In this case, the hypotenuse of each 30-60-90 right triangle is a side of the equilateral triangle; therefore, each side length of the equilateral triangle is 2k. The perimeter of a triangle is the sum of the lengths of each side. It’s given that the perimeter of the equilateral triangle 624 2 +2 +2 =624 6 =624 is ; therefore, k k k , or k . Dividing both sides of this =104 equation by 6 yields k . 47 SAT PRACTICE TEST #10 ANSWER EXPLANATIONS
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