Mrs. Aman asked her students to look at the drawing shown below to determine the length of d.Which of the following student responses best represents the length of d?
A8 units
B11 units
C14 units
D3 units
Notice that there's a right-angled triangle.
Also, notice that you're given the $\displaystyle (x, y)$ co-ordinate for where $\displaystyle d$ touches the arc.
The $\displaystyle x$ value corresponds to the horizontal distance, and the $\displaystyle y$ value corresponds to the vertical.
So, by Pythagoras...
$\displaystyle x^2 + y^2 = d^2$
$\displaystyle 4^2 + 7^2 = d^2$
$\displaystyle 16 + 49 = d^2$
$\displaystyle 65 = d^2$
$\displaystyle d = \sqrt{65}$.
Which of the students gave a measurement closest to $\displaystyle \sqrt{65}$ units?