Note: Figure NOT drawn to scale.

Note: Figure NOT drawn to scale.

Calculate the perimeter of Quadrilateral ABCD in the above diagram if:
AC = 48
BD = 20
AB = BC = CD = DA
Insufficient information is given to answer the question.
A. 120
B. 136
C. 104
D. 96

Correct Answer: C
Explanation/Reference:
Explanation:
AB = BC = CD = DA, so Quadrilateral ABCD is a rhombus. Its diagonals are therefore perpendicular to each other, and the four triangles they form are right triangles. Therefore, the Pythagorean theorem can be used to determine the common sidelength of Quadrilateral ABCD.
We focus on ΔAXB. The diagonals are also each other’s bisector, so


By the Pythagorean Theorem,

26 is the common length of the four sides of Quadrilateral ABCD, so its perimeter is 4 × 26 = 104.

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