Solve the problem.
-A rectangle that is x feet wide is inscribed in a circle of radius 16 feet. Express the area of the rectangle as a function of x.
A) $A ( x ) = x \sqrt { 768 - x }$
B) $A ( x ) = x ^ { 2 } \sqrt { 512 - x ^ { 2 } }$
C) $\mathrm { A } ( \mathrm { x } ) = \sqrt { 1024 - \mathrm { x } ^ { 2 } }$
D) $\mathrm { A } ( \mathrm { x } ) = \mathrm { x } \left( 1024 - \mathrm { x } ^ { 2 } \right)$

Question

Solve the problem.
-A rectangle that is x feet wide is inscribed in a circle of radius 16 feet. Express the area of the rectangle as a function of x. 
A) $A ( x ) = x \sqrt { 768 - x }$
B) $A ( x ) = x ^ { 2 } \sqrt { 512 - x ^ { 2 } }$
C) $\mathrm { A } ( \mathrm { x } ) = \sqrt { 1024 - \mathrm { x } ^ { 2 } }$
D) $\mathrm { A } ( \mathrm { x } ) = \mathrm { x } \left( 1024 - \mathrm { x } ^ { 2 } \right)$

Quizplus · Accepted Answer

The diagonal of the rectangle is the diameter of the circle, which is 32 feet. Using the Pythagorean theorem, the length of the rectangle can be expressed as $\sqrt{1024 - x^2}$. The area is then $x \times \sqrt{1024 - x^2}$.

Solve the Problem A(x)=x768−xA ( x ) = x \sqrt { 768 - x }A(x)=x768−x​

Solve the Problem $A ( x ) = x \sqrt { 768 - x }$