Question

student a | answer | student b

1. right triangle with legs √6, x and hypotenuse √10 | | 5. right triangle with legs x, √3 and hypotenuse √7
2. right triangle with legs 3, 5 and hypotenuse x | | 6. right triangle with legs 6, x and hypotenuse 9
3. right triangle with legs √7, √6 and hypotenuse x | | 7. right triangle with legs 6, x and hypotenuse 7
4. right triangle with legs 2, 2 and hypotenuse x | | 8. right triangle with legs √3, √5 and hypotenuse x
5. right triangle with legs x, 8 and hypotenuse √82 | | 9. right triangle with legs x, √82 and hypotenuse 10

Explanation:

Student A Problems

Problem 5:

Step1: Apply Pythagorean theorem
$(\sqrt{6})^2 + x^2 = (\sqrt{10})^2$
Step2: Simplify and solve for x
$6 + x^2 = 10 \implies x^2=4 \implies x=2$

Problem 6:

Step1: Apply Pythagorean theorem
$3^2 + 6^2 = x^2$
Step2: Simplify and solve for x
$9 + 36 = x^2 \implies x^2=45 \implies x=3\sqrt{5}$

Problem 7:

Step1: Apply Pythagorean theorem
$(\sqrt{7})^2 + (\sqrt{5})^2 = x^2$
Step2: Simplify and solve for x
$7 + 5 = x^2 \implies x^2=12 \implies x=2\sqrt{3}$

Problem 8:

Step1: Apply Pythagorean theorem
$2^2 + 2^2 = x^2$
Step2: Simplify and solve for x
$4 + 4 = x^2 \implies x^2=8 \implies x=2\sqrt{2}$

Problem 9:

Step1: Apply Pythagorean theorem
$x^2 + 8^2 = (\sqrt{82})^2$
Step2: Simplify and solve for x
$x^2 + 64 = 82 \implies x^2=18 \implies x=3\sqrt{2}$

Student B Problems

Problem 5:

Step1: Apply Pythagorean theorem
$x^2 + (\sqrt{3})^2 = (\sqrt{7})^2$
Step2: Simplify and solve for x
$x^2 + 3 = 7 \implies x^2=4 \implies x=2$

Problem 6:

Step1: Apply Pythagorean theorem
$6^2 + x^2 = 9^2$
Step2: Simplify and solve for x
$36 + x^2 = 81 \implies x^2=45 \implies x=3\sqrt{5}$

Problem 7:

Step1: Apply Pythagorean theorem
$6^2 + x^2 = 7^2$
Step2: Simplify and solve for x
$36 + x^2 = 49 \implies x^2=13 \implies x=\sqrt{13}$

Problem 8:

Step1: Apply Pythagorean theorem
$(\sqrt{3})^2 + (\sqrt{5})^2 = x^2$
Step2: Simplify and solve for x
$3 + 5 = x^2 \implies x^2=8 \implies x=2\sqrt{2}$

Problem 9:

Step1: Apply Pythagorean theorem
$x^2 + (\sqrt{82})^2 = 10^2$
Step2: Simplify and solve for x
$x^2 + 82 = 100 \implies x^2=18 \implies x=3\sqrt{2}$

Answer:

Student A

1. $2$
2. $3\sqrt{5}$
3. $2\sqrt{3}$
4. $2\sqrt{2}$
5. $3\sqrt{2}$

Student B

1. $2$
2. $3\sqrt{5}$
3. $\sqrt{13}$
4. $2\sqrt{2}$
5. $3\sqrt{2}$