Problem 14 · The squared distance AE
Adding horizontal and vertical displacements and applying Pythagoras.
Integer answer, at most 4 digitsThe figure shows a polygonal line $ABCDE$ with all right angles, and the length of each segment is given. Find the distance between points $A$ and $E$, and give the square of this number as your answer.
Copa Cangur · SCM
Easy
Closed answer
Reasoned solution
Key idea: set up coordinates along the polygonal line: every leg is horizontal or vertical.
$A = (0, 0)$; $B = (7, 0)$ (7 m right); $C = (7, -8)$ (8 m down); $D = (12, -8)$ (5 m right); $E = (12, -6)$ (2 m up).
The total displacement from $A$ to $E$ is $12$ horizontally and $8 - 2 = 6$ vertically. By Pythagoras:
$$AE^{2} = 12^{2} + 6^{2} = 144 + 36 = 180.$$
Answer: 180