what do you get when you cross a computer with a lifeguard?
write the letter of each answer in the box containing the exercise number.
complete the sentence.

in a(n) ______ triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

a(n) ______ triple is a set of three positive integers, $a$, $b$, and $c$, that satisfy the equation $c^{2}=a^{2}+b^{2}$.

if the square of the length of the ______ side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

for any $\triangle abc$, where $c$ is the length of the longest side, if $c^{2}
for any $\triangle abc$, where $c$ is the length of the longest side, if $c^{2}>a^{2}+b^{2}$, then $\triangle abc$ is ______.

find the value of $x$.

$a = 20$, $b = 99$

$a = 60$, $b = 91$

classify the triangle based on the given side lengths. for your answer, use \1\ for acute, \2\ for obtuse, and \3\ for right.

20, 21, and 29

15, 19, and 24

11, 23, and 26

find the value of $x$.

$a = x$, $b = 45$, $c = 53$

$a = 9$, $b = x$, $c = 41$

answers
v. 1
b. equilateral
s. acute
s. 2
n. obtuse
i. angle
e. 101
h. special
r. right
k. null
u. $\sqrt{101}$
a. 40
m. 113
e. 109
o. shortest
c. 28
c. 36
r. longest
a. pythagorean
t. 98
e. 3

Question

what do you get when you cross a computer with a lifeguard?
write the letter of each answer in the box containing the exercise number.
complete the sentence.
1. in a(n) ______ triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
2. a(n) ______ triple is a set of three positive integers, $a$, $b$, and $c$, that satisfy the equation $c^{2}=a^{2}+b^{2}$.
3. if the square of the length of the ______ side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.
4. for any $\triangle abc$, where $c$ is the length of the longest side, if $c^{2}<a^{2}+b^{2}$, then $\triangle abc$ is ______.
5. for any $\triangle abc$, where $c$ is the length of the longest side, if $c^{2}>a^{2}+b^{2}$, then $\triangle abc$ is ______.
find the value of $x$.
6. $a = 20$, $b = 99$
7. $a = 60$, $b = 91$
classify the triangle based on the given side lengths. for your answer, use \1\ for acute, \2\ for obtuse, and \3\ for right.
8. 20, 21, and 29
9. 15, 19, and 24
10. 11, 23, and 26
find the value of $x$.
11. $a = x$, $b = 45$, $c = 53$
12. $a = 9$, $b = x$, $c = 41$
answers
v. 1
b. equilateral
s. acute
s. 2
n. obtuse
i. angle
e. 101
h. special
r. right
k. null
u. $\sqrt{101}$
a. 40
m. 113
e. 109
o. shortest
c. 28
c. 36
r. longest
a. pythagorean
t. 98
e. 3

Accepted Answer

# Explanation: ## Step1: Match term to right triangle Definition of right triangle: In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs. Answer for 1: R. right ## Step2: Match term to integer triple Definition of Pythagorean triple: A set of 3 positive integers satisfying $c^2=a^2+b^2$. Answer for 2: A. Pythagorean ## Step3: Identify triangle side condition For right triangle, the square of the longest side equals sum of squares of other two sides. Answer for 3: R. longest ## Step4: Classify triangle by side relation If $c^2 < a^2 + b^2$, triangle is acute. Answer for 4: S. acute ## Step5: Classify triangle by side relation If $c^2 > a^2 + b^2$, triangle is obtuse. Answer for 5: N. obtuse ## Step6: Calculate hypotenuse via Pythagoras Use $x=\sqrt{a^2+b^2}$, substitute $a=20,b=99$: $x=\sqrt{20^2+99^2}=\sqrt{400+9801}=\sqrt{10201}=101$ Answer for 6: E. 101 ## Step7: Calculate hypotenuse via Pythagoras Use $x=\sqrt{a^2+b^2}$, substitute $a=60,b=91$: $x=\sqrt{60^2+91^2}=\sqrt{3600+8281}=\sqrt{11881}=109$ Answer for 7: E. 109 ## Step8: Classify triangle via side relation Check $29^2=841$, $20^2+21^2=400+441=841$. Since $c^2=a^2+b^2$, it is right (code 3). Answer for 8: E. 3 ## Step9: Classify triangle via side relation Check $24^2=576$, $15^2+19^2=225+361=586$. Since $c^2 < a^2 + b^2$, it is acute (code 1). Answer for 9: V. 1 ## Step10: Classify triangle via side relation Check $26^2=676$, $11^2+23^2=121+529=650$. Since $c^2 > a^2 + b^2$, it is obtuse (code 2). Answer for 10: S. 2 ## Step11: Calculate leg via Pythagoras Use $x=\sqrt{c^2-b^2}$, substitute $b=45,c=53$: $x=\sqrt{53^2-45^2}=\sqrt{2809-2025}=\sqrt{784}=28$ Answer for 11: C. 28 ## Step12: Calculate leg via Pythagoras Use $x=\sqrt{c^2-a^2}$, substitute $a=9,c=41$: $x=\sqrt{41^2-9^2}=\sqrt{1681-81}=\sqrt{1600}=40$ Answer for 12: A. 40 # Answer: 1. R. right 2. A. Pythagorean 3. R. longest 4. S. acute 5. N. obtuse 6. E. 101 7. E. 109 8. E. 3 9. V. 1 10. S. 2 11. C. 28 12. A. 40 (When filling the bottom boxes in order 12,4,11,1,6,8,5,10,2,9,7,3: A, S, C, R, E, E, N, S, A, V, E, R → spells **A SCREEN SAVER**)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Match term to right triangle

Answer:

Step2: Match term to integer triple