Question

9.1 puzzle time
what do you get when you cross a com
with a lifeguard?
write the letter of each answer in the box containing the exercise n
complete the sentence.

1. in a(n) right triangle, the square of the length of the

hypotenuse is equal to the sum of the squares of the lengths
of the legs.

1. a(n) ______ triple is a set of three positive integers, a, b,

and c, that satisfy the equation ( c^2 = a^2 + b^2 ).

1. 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.

1. for any ( \triangle abc ), where c is the length of the longest side,

if ( c^2 < a^2 + b^2 ), then ( \triangle abc ) is ______.

1. for any ( \triangle abc ), where c is the ______ of the longest side,

if ( c^2 > a^2 + b^2 ), then ( \triangle abc ) is obtuse.
find the value of x.

1. ( a = 20, b = 99 ); find x.
2. ( a = 60, b = 91 ); find x.

(diagram: right triangle with legs a, b, hypotenuse x)
given the side lengths, determine whether the triangle is (1) ac

1. 20, 21, and 29
2. 15, 19, and 24

find the value of x.

1. ( a = x, b = 45, c = 53 )
2. ( a = 9, b = x, c = 41 )

(diagram: right triangle with legs a, b, hypotenuse c)
(answer box with numbers 12, 4, 11, 1, ...)

Explanation:

Let's solve question 6: \(a = 20\), \(b = 99\), find \(x\) (hypotenuse of a right triangle).

Step 1: Recall the Pythagorean theorem

For a right triangle, \(x^{2}=a^{2}+b^{2}\), where \(x\) is the hypotenuse, and \(a\), \(b\) are the legs.
Substitute \(a = 20\) and \(b = 99\) into the formula: \(x^{2}=20^{2}+99^{2}\)

Step 2: Calculate the squares

\(20^{2}=400\), \(99^{2}=9801\)
So, \(x^{2}=400 + 9801=10201\)

Step 3: Take the square root

\(x=\sqrt{10201}\)
Since \(101\times101 = 10201\), we have \(x = 101\)

Answer:

\(x = 101\)