SAT Math Multiple Choice Practice Question 433: Answer and Explanation
16. An equilateral triangle has sides of length x. If a second equillateral triangle has sides of length 2x, what is the ratio of the area of the first triangle to the area of the second?
A. 1 : 16
B. : 2
C. 1 : 2
D. 1 : 4
E. 1 :
Correct Answer: D
D Since each side is a mysterious "x long," let's make up a value for x to make our lives a little easier. Let's use 10, just because it's nice and round. To find the area of the first triangle, you'll have to find the height, which is the middle side of a 30°-60°-90° triangle. If the entire base is 10, then the height is 5. The area is then A = bh = 10(5) = 25. The second triangle has side lengths of 2x, which means each side is 20 long. We can find the area in the same way as the first one. We'll end up with a height of 10, and the area is 20(10) = 100. Since the area of the second triangle is four times the area of the first one, the answer is D, 1 : 4.