Question

Which set of numbers could not represent the lengths of the sides of a right triangles?

A. {1, 3, sqrt10}

B. {2, 3, 4}

C. {3, 4, 5}

D. {8, 15, 17}

Answer 1

Answer:

B. 2,3,4

Step-by-step explanation:

Using the Pythagorean Theorem:

A. 1^2+3^2=(sqrt10^2)

B. 2^2+3^2not equal to 4^2

C. 3^3+4^2=5^2

D. 8^2+15^2=17^2

Answer 2

The set of numbers {2, 3, 4} could not represent the lengths of the sides of a right triangles.

The correct option is an option (B).

What is Pythagorean triples?

"For integers a, b, c if a² + b² = c², then these integers are called as Pythagorean triples they can be denoted as (a, b, c)"

What is Pythagoras theorem?

"For a right triangle,

c² = a² + b², where c is the hypotenuse and a, b are any two sides of the right triangle."

What is hypotenuse?

"It is the lonest side of the right triangle."

For given example,

We need to find the set of numbers that could not represent the lengths of the sides of a right triangles.

If the set of numbers is not Pythagorean triple then it would not represent the lengths of the sides of a right triangles.

A) {1, 3, √10}

let a = 1, b = 3, c = √10

⇒ c² = (√10)²

⇒ c² = 10

Consider, a² + b² = 1² + 3²

⇒ a² + b² = 1 + 9

⇒ a² + b² = 10

⇒ a² + b² = c²

This means, these numbers are Pythagorean triple.

So, these numbers represents the lengths of the sides of the right triangle with hypotenuse √10 unit and other two sides are 1 unit and 3 units.

B) {2 ,3, 4}

let a = 2, b = 3, c = 4

⇒ c² = (4)²

⇒ c² = 16

Consider, a² + b² = 2² + 3²

⇒ a² + b² = 4 + 9

⇒ a² + b² = 13

⇒ a² + b² ≠ c²

This means, these numbers are not a Pythagorean triple.

So, these numbers does not represent the lengths of the sides of the right triangle.

C) {3, 4, 5}

let a = 3, b = 4, c = 5

⇒ c² = (5)²

⇒ c² = 25

Consider, a² + b² = 3² + 4²

⇒ a² + b² = 9 + 16

⇒ a² + b² = 25

⇒ a² + b² = c²

This means, these numbers are Pythagorean triple.

Hence, these numbers represents the lengths of the sides of the right triangle with hypotenuse 5 units and other two sides are 3 units and 4 units.

D) {8, 15, 17}

let a = 8, b = 15, c = 17

⇒ c² = (17)²

⇒ c² = 289

Consider, a² + b² = 8² + 15²

⇒ a² + b² = 64 + 225

⇒ a² + b² = 289

⇒ a² + b² = c²

This means, these numbers are Pythagorean triple.

So, these numbers represents the lengths of the sides of the right triangle with hypotenuse 17 units and other two sides are 8 units and 15 units.

Therefore, the set of numbers {2, 3, 4} could not represent the lengths of the sides of a right triangles.

The correct option is an option (B).

Learn more about Pythagorean triple here:

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