Question

Which side lengths form a right triangle? Choose all answers that apply: Choose all answers that apply: (Choice A) A 5, 12, 135,12,135, comma, 12, comma, 13 (Choice B) B 4, 4, 84,4,84, comma, 4, comma, 8 (Choice C) C 2, 3, 42,3,4

Answer 1

Option A) 5, 12, 13 is a right angle triangle.

Option C) 2, 3, 4 is approximately a right angle triangle.

Explanation:

A right angle triangle always follow pythagora's theorem which basically states that the addition of the squares of the two smaller sides must give the square of the largest side.

For option A)

5^2 + 12^2 = 25 + 144 = 169

Square root of 169 is 13, so it's correct.

For option B)

4^2 + 4^2 = 16 + 16 = 32

Square root of 32 is 5.65, which is not equal to 8. This is not a right angle triangle.

For option C)

2^2 + 3^2 = 4 + 9 = 13

Square root of 13 is 3.606, approximately 4. So this is approximately a right angle triangle.

If the answer requires that it must be exact then choose only A, Otherwise, A and C are correct.

Answer 2

Answer: option A is correct

Explanation:

The given side lengths are

A) 5, 12, 13

B) 4, 4, 8

C) 2, 3, 4

To be able to form a right ange triangle, the given side lengths must be a Pythagorean triple. Pythagorean triple obeys the Pythagorean theorem such that

Hypotenuse² = opposite side² + adjacent side²

Hypotenuse = the longest side

Applying it to the given options,

A) 13² = 5² + 12² = 25 + 144

169 = 169

It forms a right angle triangle

B) 8² = 4² + 4² = 16 + 16

64 ≠ 32

It does not forms a right angle triangle

C) 4² = 3² + 2²

16 ≠ 13

It does not forms a right angle triangle