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The perimeter of an equilateral triangle is 852 centimeters. The three vertices of the triangle lie on a circle. The radius of the circle is w 3 centimeters. What is the value of w? OP
Correct answer: 3 (parsed from the explanation — this source omits an answer key for this item)
Explanation
284 The correct answer is 3 . Since the perimeter of a triangle is the sum of the lengths of its sides, and the given triangle is equilateral, the length of each side is 852 284 3 , or , centimeters (cm). Right triangle AMO can be formed, where M is the midpoint of one of the triangle’s sides, A is one of this side’s endpoints, and O is 284 142 the center of the circle. It follows that AM is 2 , or , cm. Additionally, 30c 60c 90c triangle AMO has angles measuring , , and , where the measure of 90c 30c angle OMA is and the measure of angle OAM is . It follows that the length 39 SAT PRACTICE TEST #8 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 1 of side MO is half the length of hypotenuse AO, and the length of side AM is = 3 times the length of side MO. It’s given that AO w 3 cm. Therefore, 3 3 3 3 MO =w 2 cm and AM =w 2 cm, which is equivalent to AM = 2w cm. Since AM =142 cm, it follows that 3 2w=142 . Multiplying both sides of this equation by 2 3 =284 = 284 yields w . Dividing both sides of this equation by 3 yields w 3 . Note that 284/3, 94.66, and 94.67 are examples of ways to enter a correct answer. 40 SAT PRACTICE TEST #8 ANSWER EXPLANATIONS
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