sat suite question viewer
In the figure shown, triangle is similar to triangle , where corresponds to and corresponds to . The length of is , and the perimeter of triangle is . The length of is . What is the perimeter of triangle ?
Explanation
Choice A is correct. It’s given that triangle is similar to triangle , where corresponds to and corresponds to . It follows that corresponds to . If two triangles are similar, then the scale factor between their perimeters is equal to the scale factor between the lengths of their corresponding sides. It's given that the length of is and the length of is . Therefore, the scale factor from the length of to the length of is , or . It’s given that the perimeter of triangle is . Let represent the perimeter of triangle . It follows that . Multiplying each side of this equation by yields . Therefore, the perimeter of triangle is .
Choice B is incorrect and may result from conceptual or calculation errors.
Choice C is incorrect and may result from conceptual or calculation errors.
Choice D is incorrect and may result from conceptual or calculation errors.