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 __ of the longest side, if ( c^2 > a^2 + b^2 ), then ( \triangle abc ) is obtuse. find the value of x. 6. ( a = 20, b = 99 ); find x. 7. ( a = 60, b = 91 ); find x. image of right triangle with legs a, b, hypotenuse x given the side lengths, determine whether the triangle is (1) 8. 20, 21, and 29 9. 15, 19, and 24 find the value of x. 11. ( a = x, b = 45, c = 53 ) 12. ( a = 9, b = x, c = 41 ) image of right triangle with legs a, b, hypotenuse c

Explanation:

Problem 6:

Step1: Identify the formula (Pythagorean theorem)

For a right triangle, \( x^{2}=a^{2}+b^{2} \), where \( a = 20 \), \( b=99 \).

Step2: Substitute values

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

Step3: Take square root

\( x=\sqrt{10201}=101 \)

Step1: Use Pythagorean theorem

\( x^{2}=a^{2}+b^{2} \), \( a = 60 \), \( b = 91 \)

Step2: Calculate \( a^{2}+b^{2} \)

\( 60^{2}+91^{2}=3600+8281 = 11881 \)

Step3: Find square root

\( x=\sqrt{11881}=109 \)

Step1: Identify the longest side

Longest side is \( 29 \), so check \( 29^{2}\) vs \( 20^{2}+21^{2} \)

Step2: Calculate both sides

\( 29^{2}=841 \), \( 20^{2}+21^{2}=400 + 441=841 \)

Step3: Determine triangle type

Since \( 29^{2}=20^{2}+21^{2} \), it's a right triangle.

Answer:

\( 101 \)

Problem 7: