Question

1. use a pythagorean triple or the pythagorean theorem to find the missing side length of the right triangle given two side lengths:
2. ______,15,17
3. 6,8,______
4. 3,4,______
5. ______,24,26
6. 5,______,13

a. 5
b. 8
c. 12
d. 10

Explanation:

Step1: Recall Pythagorean Theorem

For a right triangle with sides $a, b, c$ (where $c$ is hypotenuse): $a^2 + b^2 = c^2$

Step2: Solve Q1: _,15,17

Check if 15,17 are legs/hypotenuse: $17^2 - 15^2 = 289 - 225 = 64 = 8^2$

Step3: Solve Q2: 6,8,_

Calculate hypotenuse: $6^2 + 8^2 = 36 + 64 = 100 = 10^2$

Step4: Solve Q3: 3,4,_

Calculate hypotenuse: $3^2 + 4^2 = 9 + 16 = 25 = 5^2$

Step5: Solve Q4: _,24,26

Check if 24,26 are legs/hypotenuse: $26^2 - 24^2 = 676 - 576 = 100 = 10^2$ (or recognize scaled triple: 10,24,26 is 2×5,12,13)
Wait correction: $26^2 - 24^2 = (26-24)(26+24)=2×50=100=10^2$. Alternatively, if checking missing leg: $26^2-24^2=100=10^2$.

Step6: Solve Q5:5,_,13

Check if 5,13 are legs/hypotenuse: $13^2 - 5^2 = 169 - 25 = 144 = 12^2$

Answer:

1. b. 8
2. d. 10
3. a. 5
4. d. 10
5. c. 12