A 9x12 rectangle is inscribed in a circle. What is the radius of the circle?

Thanks Heureka,

I am going to do it a little differently but our answers are the same :)

A 9x12 rectangle is inscribed in a circle. What is the radius of the circle?

The diagonal of the rectangle is the hypotenuse of the triangle with short sides 9 and 12

It is also the diameter of the circle.

$$\\d^2=9^2+12^2\\
d^2=81+144\\
d^2=225\\
d=15\\
$The radius is half the diameter so radius = 7.5 units$$$

You might have got this straight of if you had realised that

3*3=9

4*3=12

5*3=15

3,4,5 is a pythagorean triad so, so is 9,12,15.     So the diameter had to be 15units

A 9x12 rectangle is inscribed in a circle. What is the radius of the circle ?

$$\small{\text{$
\begin{array}{rcl}
r^2 &=& \left(\dfrac{9}{2}\right)^2+ \left(\dfrac{12}{2}\right)^2\\\\
r^2 &=& 4.5^2+6^2\\\\
r^2 &=& 56.25 \\\\
r &=& \sqrt{56.25 }\\\\
\mathbf{r} & \mathbf{=} & \mathbf{7.5}
\end{array}
$}}$$