Question

start
finish!
find the length of each right triangle to make it correctly through the maze. shade or color your path as you go.
$a=5$
$b=12$
$c=?$
$a=15$
$b=20$
$c=?$
$a=21$
$b=28$
$c=?$
$a=9$
$b=40$
$c=?$
$a=8$
$b=?$
$c=17$
$a=?$
$b=12$
$c=15$
$a=20$
$b=?$
$c=29$
$a=?$
$b=16$
$c=20$
$a=3$
$b=4$
$c=?$
$a=7$
$b=24$
$c=?$
$a=6$
$b=?$
$c=10$

Explanation:

We use the Pythagorean theorem for right triangles: $a^2 + b^2 = c^2$ (where $c$ is the hypotenuse, $a,b$ are legs) to solve each step and follow the maze path.

Step1: Start, solve for $c$

$a=5, b=12$, so $c=\sqrt{5^2+12^2}=\sqrt{25+144}=\sqrt{169}=13$

Step2: Move to next, solve for $b$

$a=8, c=17$, so $b=\sqrt{17^2-8^2}=\sqrt{289-64}=\sqrt{225}=15$

Step3: Move to next, solve for $a$

$b=12, c=15$, so $a=\sqrt{15^2-12^2}=\sqrt{225-144}=\sqrt{81}=9$

Step4: Move to next, solve for $c$

$a=3, b=4$, so $c=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5$

Step5: Reach FINISH via matching value 5

Answer:

The correct path through the maze is:

1. Start ($a=5, b=12$) → calculate $c=13$ → move to the diamond labeled 13
2. Next box ($a=8, c=17$) → calculate $b=15$ → move to the diamond labeled 15
3. Next box ($b=12, c=15$) → calculate $a=9$ → move to the diamond labeled 9
4. Next box ($a=3, b=4$) → calculate $c=5$ → move to the diamond labeled 5
5. Arrive at FINISH!

Calculated values for each step:

• $c=13$ (start)
• $b=15$
• $a=9$
• $c=5$