grandh01 wrote:What is the area of the rectangular field?
1) The diagonal is twice the width.
2) Length = 173 feet
OA IS C
The diagonal of a rectangle splits the rectangle into two congruent right triangles.
The diagonal of the rectangle = the hypotenuse each right triangle.
Statement 1: The diagonal is twice the width
ALWAYS LOOK FOR SPECIAL TRIANGLES.
In a 30-60-90 triangle, the sides are in the following ratio:
x : x√3 :
2x.
Note the values in red.
If the hypotenuse of a right triangle is twice one of the legs, the triangle is a 30-60-90 triangle.
Since the diagonal here is twice the width of the rectangle, the diagonal splits the rectangle into two 30-60-90 triangles.
No way to determine any exact lengths.
INSUFFICIENT.
Statement 2: Length = 173 feet
No way to determine the width.
INSUFFICIENT.
Statement 1 and 2 combined:
The length of the rectangle = 173 = the length of the longer leg of each 30-60-90 triangle.
Since x√3 = 173, x = 173/√3.
Thus, the area of the rectangle can be determined.
SUFFICIENT.
The correct answer is
C.
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