SAT Math Multiple Choice Practice Question 263: Answer and Explanation

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Question: 263

21. An equilateral triangle with area square centimeters is divided into two triangles by the bisector of one of its angles. What is the sum of the perimeters of these two triangles?

A.
B.
C.
D.
E.

Correct Answer: D

Explanation:

D First draw a diagram to see how the area of an equilateral triangle is related to the lengths of the sides:

Notice that the height (which is also the bisector of the "top" angle) divides the triangle into two 30° 60°-90° triangles, with sides as shown. The area of a triangle is base × height/2, which in this case is

Since the area is given as, x must equal 6. Substituting this into the diagram, each smaller triangle has sides of length 6, and 12. Therefore the sum of the perimeters of the two triangles is

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