Question

A rectangle with one side equal to 6 cm is inscribed in a circle of radius 5 cm. Then what is the area of the rectangle?

• A. $36c{m}^2$
• B. $42c{m}^2$
• C. $48c{m}^2$
• D. $54c{m}^2$

Answer 1

The correct option is C $48c{m}^2$

Since the radius is $5$, the diameter is $10$.
A diagonal for the rectangle is equal to this diameter.
We have a triangle with side lengths of $10$ and $6$.
$10$ is the hypotenuse. Set x = the length of the
other side of the triangle.
so $6^2+x^2={10}^2$
$36+x^2=100$
$x^2$ = $64$
$x$ = $8$
We have side lengths of $6$ and $4$ so
the area = $6\times 8$ = $48$ sq. cm