Question

a rectangle with vertices (0, 0), (0, 6), (12, 6), and (12, 0) is shown on a coordinate plane.
what is the length of the diagonal of the rectangle, rounded to the nearest hundredth of a unit?

Explanation:

Step1: Identify rectangle side lengths

The rectangle has width $12$ (from $x=0$ to $x=12$) and height $6$ (from $y=0$ to $y=6$).

Step2: Apply Pythagorean theorem

For diagonal $d$, use $d=\sqrt{w^2+h^2}$ where $w=12$, $h=6$.
$$d=\sqrt{12^2 + 6^2}$$

Step3: Calculate inside the square root

$$12^2 + 6^2 = 144 + 36 = 180$$

Step4: Compute square root and round

$$d=\sqrt{180} \approx 13.416$$
Round to nearest hundredth: $13.42$

Answer:

13.42