Solve the problem.
-A rectangle that is x feet wide is inscribed in a circle of radius 36 feet. Express the area of the rectangle as a function of x.
A) $A ( x ) = x ^ { 2 } \sqrt { 2,592 - x ^ { 2 } }$
B) $A ( x ) = x \sqrt { 5,184 - x ^ { 2 } }$
C) $A ( x ) = x \left( 5,184 - x ^ { 2 } \right)$
D) $A ( x ) = x \sqrt { 3,888 - x }$

Question

Quizplus · Accepted Answer

The diameter of the circle is the diagonal of the rectangle, which is $2 \times 36 = 72$ feet. By the Pythagorean theorem, if $x$ is the width, then the height $h$ of the rectangle can be found from $x^2 + h^2 = 72^2$. Solving for $h$, we get $h = \sqrt{72^2 - x^2}$. The area of the rectangle is $A(x) = x \cdot h = x \cdot \sqrt{72^2 - x^2} = x \cdot \sqrt{5184 - x^2}$.

Solve the Problem A(x)=x22,592−x2A ( x ) = x ^ { 2 } \sqrt { 2,592 - x ^ { 2 } }A(x)=x22,592−x2​

Solve the Problem $A ( x ) = x ^ { 2 } \sqrt { 2,592 - x ^ { 2 } }$