instruction:
You are given a geometric mathematical question. Questions in this task often involve shapes and Geometric Relationships. You are also given 4 or 5 answer options (associated with "A", "B", "C", "D", "E"). Do not generate anything else apart from one of the following characters: 'A', 'B, 'C', 'D', 'E'. LaTeX mathematical format (the standard way to express mathematical expressions in the typesetting software known as LaTeX) is used to express equations. Each question is solvable with high school math knowledge.
question:
If a square and an equilateral triangle have equal perimeters, what is the ratio of the area of the triangle to the area of the square?
(A)\(\frac { 4\sqrt { 3 } } { 9 } \) (B)\(\frac { 4 } { 9 } \) (C)\(\frac { 3 } { 4 } \) (D)\(\frac { 1 } { 1 } \) (E)\(\frac { 4 } { 3 } \)
answer:
A


question:
If \(c(x) = x^2 - 6\), how many times does the graph of \(c(x)\) cross the x-axis?
(A)0 (B)1 (C)2 (D)3 (E)4
answer:
C


question:
A rectangular swimming pool has a volume of 8,640 cubic feet. If its length is 60 feet and its depth is 6 feet, what is the width of the pool in feet?
(A)16 (B)19 (C)24 (D)28 (E)36
answer:

C