Data Sufficiency for Land Area

Question

A farmer has a quadrilateral parcel of land with a perimeter of 700 feet. Two opposite angles of that parcel of land are right angles, while the remaining two are not. The farmer wants to do organic farming on that parcel of land. The cost of organic farming is Rs. 400 per square foot. Consider the following two additional pieces of information: I. The length of one of the sides of that parcel of land is 110 feet. II. The distance between the two corner points where the non-perpendicular sides o

Accepted Answer

C. Let $ABCD$ be the quadrilateral with right angles at $A$ and $C$. Then the diagonal $BD$ is the common hypotenuse of right triangles $ABD$ and $CBD$. From II, diagonal $BD = 255$. From I, $AD = 110$. In $	riangle ABD$, $AB = \sqrt{255^2 - 110^2} \approx 230$. Then $BC + CD = 700 - 110 - 230 = 360$. Also $BC^2 + CD^2 = BD^2 = 255^2$. We can uniquely determine $BC$ and $CD$, and thus calculate the areas of both right triangles $	riangle ABD$ and $	riangle CBD$, giving the total area and total cost. Neither statement alone is sufficient, but both together are minimally sufficient.

Answer

II only

Answer

I only

Answer

I and II together only

Answer

Either of I or II, by itself

Answer

The amount cannot be determined even with the additional pieces of information.

Data Sufficiency for Land Area

Explanation

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