Which of these sets could represent the side lengths of a right triangle?

Group of answer choices

{4, 8, 12}

{6, 8, 10}

{6, 8, 15}

{5, 7, 13}

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Question 31 pts

At the electronics store, television screens are sized by the lengths of their diagonals. The television that Mrs. Mallory wants to buy has a 25 inch diagonal. The width of the screen is 15 inches. What is the height of the screen?

Group of answer choices

10 inches

15 inches

20 inches

25 inches

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Question 41 pts

Determine the missing length. Round to the nearest foot.

Unit 3 test - 1. gif

Group of answer choices

115 feet

467 feet

472 feet

504 feet

Answer: Question 41 is 467

Step-by-step explanation:

Pythagorean theorem

for the first question:

Which of these sets could represent the side lengths of a right triangle?

{4, 8, 12}

{6, 8, 10}

{6, 8, 15}

{5, 7, 13}

you must use pythagorean theorem to find the answer: a²+b²=c²

so in this case 4²+8² should equal 12²

4²=16

8²=64

12²=144

if 4²+8² should equal 12² then 16+64 should equal 144 but it does not

16+64=80 therefore the first option is not a right triangle.

{6, 8, 10}

6²+8² should equal 10²

6²=36

8²=64

10²=100

36+64=100

therefore ... this is the correct answer. i'll do the other options to prove that this is correct though.

{6, 8, 15} we know this is wrong because we just found that 6²+8² is equal to 10²

how could it equal both 10² AND 15²? it can't

{5, 7, 13}

5²=25

7²=49

13²=169

25+49=74

this is wrong

{6, 8, 10} is the answer

Question 31:

At the electronics store, television screens are sized by the lengths of their diagonals. The television that Mrs. Mallory wants to buy has a 25 inch diagonal. The width of the screen is 15 inches. What is the height of the screen?

If you were cut a rectangle in half from corner to corner, you would have two triangles. The hypotenuse is the diagonal line that you cut, which is 25in²

and the width of the triangle is 15in²

25²-15²=400

25²=625

15²=225

625-225=400

25²-15²=400

square root of 400=20

how do we know if 20 inches is correct? we add

20²+15²=

20²=400

15²=225

400+225=625

20²+15²=25²! therefore the equation is correct!

20 inches is the answer

Question 41

Determine the missing length. Round to the nearest foot.

320²+340²=c²

320²=102,400

340²=115,600

102,400 + 115,600 = 218,000

square root of 218,000=466.9

rounded to nearest foot is 467