Question

Which triangle side lengths form a right triangle? Choose all that apply. -5,6,7 , 6,8,10 , 8,15,17 , 10,12,15 , 15,20,25 , 16,18,20

Answer 1

Answer: The triangle side lengths that will form a right triangle are 6,8,10 , 8,15,17 and 15,20,25

Step-by-step explanation:

For a right angle, the square of the largest number must be equal to the square of the two smaller numbers gicen. The hypotenuse is the largest side and its square must be equal to the addition of the square of the "adjacent" and the"opposite".

a. 5,6,7

= 5^2 + 6^2

= 25 + 36

= 61

7^2= 7 × 7

= 49

Since the numbers gotten are different, it's not a right angle.

b. 6,8,10

= 6^2 + 8^2

= 36 + 64

= 100

10^2 = 10 × 10

= 100

Since the numbers gotten are the same, it's a right angle.

c. 8,15,17

= 8^2 + 15^2

= 64 + 225

= 289

17^2 = 17 × 17

= 289

Since the numbers gotten are the same, it's a right angle.

d. 10,12,15

= 10^2+ 12^2

= 100 + 144

= 244

15^2

= 15 × 15

= 225

Since the numbers gotten are different, it's not a right angle.

e. 15,20,25

= 15^2 + 20^2

= 225 + 400

= 625

25^2 = 25 × 25

= 625

Since the numbers gotten are the same, it's a right angle.

f. 16,18,20

= 16^2 + 18^2

= 256 + 324

= 580

20^2= 20 × 20

= 400

Since the numbers gotten are different, it's not a right angle.

Therefore, the triangle side lengths that will form a right triangle are 6,8,10 , 8,15,17 and 15,20,25.

Answer 2

Answer:

(6,8 and 10), (8,15,17) and (15,20,25) will form right triangle

Step-by-step explanation:

In this question, we are concerned about which of the options given in the question will work.

Now, this brings us to a new definition. This new definition is called the pythagorean triple.

When we talk about these triplets, we are taking about a set of 3 numbers such that the number in these sets form the length of the sides of the triangle perfectly.

This means the set have the hypotenuse, the adjacent and opposite. To identify a pythagorean triple, squaring each of the two lesser numbers, and adding them together gives the square of the largest number.

A quick example of a pythagorean triple is the set (3,4 and 5)

Squaring 3 and 4 gives 9 and 16 respectively. Now, by adding these values together, we get 25 which is the square of the largest number 5

From the options, (6,8,10) is a triple , (8,15,17) is a triple, (15,20,25) is a triple also

What all these options have in common is that by adding the squares of the two lesser number will give the square of the biggest number.