Question

maze #1
date ______________________pd__
find the missing side length of each right triangle to make it correctly through the maze. shade or color your path as you go.
start
$a = 5$
$b = 12$
$c = ?$
$a = 15$
$b = 20$
$c = ?$
$a = 21$
$b = 28$
$c = ?$
$a = 9$
$b = 40$
$c = ?$
$a = 8$
$b = ?$
$c = 17$
$a = ?$
$b = 12$
$c = 15$
$a = 20$
$b = ?$
$c = 29$
$a = ?$
$b = 16$
$c = 20$
$a = 3$
$b = 4$
$c = ?$
$a = 7$
$b = 24$
$c = ?$
$a = 6$
$b = ?$
$c = 10$
finish!

Explanation:

We use the Pythagorean theorem for right triangles: $c^2 = a^2 + b^2$ (for finding hypotenuse $c$), or $a^2 = c^2 - b^2$, $b^2 = c^2 - a^2$ (for finding legs).

Step1: Start with first triangle

Find $c$ for $a=5, b=12$.
$c = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13$
Path: move to the diamond labeled 13, then to the next triangle

Step2: Solve $a=8, c=17$

Find $b$ using $b = \sqrt{c^2 - a^2}$.
$b = \sqrt{17^2 - 8^2} = \sqrt{289 - 64} = \sqrt{225} = 15$
Path: move to the diamond labeled 15, then to the next triangle

Step3: Solve $a=15, b=20$

Find $c$ using $c = \sqrt{a^2 + b^2}$.
$c = \sqrt{15^2 + 20^2} = \sqrt{225 + 400} = \sqrt{625} = 25$
Path: move to the diamond labeled 25, then to the next triangle

Step4: Solve $a=?, b=12, c=15$

Find $a$ using $a = \sqrt{c^2 - b^2}$.
$a = \sqrt{15^2 - 12^2} = \sqrt{225 - 144} = \sqrt{81} = 9$
Path: move to the diamond labeled 9, then to the next triangle

Step5: Solve $a=3, b=4$

Find $c$ using $c = \sqrt{a^2 + b^2}$.
$c = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$
Path: move to the diamond labeled 5, then to FINISH!

Answer:

The correct path through the maze is:

1. Start → $a=5,b=12,c=13$ → Diamond 13
2. → $a=8,b=15,c=17$ → Diamond 15
3. → $a=15,b=20,c=25$ → Diamond 25
4. → $a=9,b=12,c=15$ → Diamond 9
5. → $a=3,b=4,c=5$ → Diamond 5 → FINISH!

The solved missing values are:

• $c=13$ (first triangle)
• $b=15$ (second triangle)
• $c=25$ (third triangle)
• $a=9$ (fourth triangle)
• $c=5$ (final triangle)