How to find the length of the side of a rectangle - ISEE Upper Level (grades 9-12) Quantitative Reasoning

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Question

Note: Figure NOT drawn to scale

The above figure shows Rhombus .

Which is the greater quantity?

(a)

(b)

Answer

The opposite sides of a parallelogram - a rhombus included - are congruent, so

.

Also, Quadrilateral form a rectangle; since $\overline{AX} || \overline{CY}$ and $\overline{AY} \perp \overline{CY}$ , it follows that $\overline{AY} \perp \overline{AX}$ , and, similarly, $\overline{XC} \perp \overline{CY}$ . Therefore, , and

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