Solve the Problem $$y = 4 - x ^ { 2 }$$

Multiple Choice

Solve the problem.
-A rectangle is bounded by the x-axis and a parabola defined by $$y = 4 - x ^ { 2 }$$ . What are the dimensions of the rectangle if the area is $6 \mathrm {~cm} ^ { 2 }$ ? Assume that all units of length are in centimeters.

A) $2 \mathrm {~cm}$ by $3 \mathrm {~cm}$
B) $\sqrt { 13 } - 1 \mathrm {~cm}$ by $\frac { 1 + \sqrt { 13 } } { 2 } \mathrm {~cm}$
C) $1 \mathrm {~cm}$ by $6 \mathrm {~cm}$ or $\frac { \sqrt { 13 } - 1 } { 2 }$ by $\frac { 1 + \sqrt { 13 } } { 2 } \mathrm {~cm}$
D) $2 \mathrm {~cm}$ by $3 \mathrm {~cm}$ or $\sqrt { 13 } - 1 \mathrm {~cm}$ by $\frac { 1 + \sqrt { 13 } } { 2 } \mathrm {~cm}$