Question

Which of the following are true statements.

The lengths 7, 40 and 41 can not be sides of a right triangle. The lengths 12, 16, and 20 can not be sides of a right triangle.

The lengths 7, 40 and 41 can not be sides of a right triangle. The lengths 12, 16, and 20 can be sides of a right triangle.

The lengths 7, 40 and 41 can be sides of a right triangle. The lengths 12, 16, and 20 can not be sides of a right triangle.

The lengths 7, 40 and 41 can be sides of a right triangle. The lengths 12, 16, and 20 can be sides of a right triangle.

Answer 1

Second statement is true.

The lengths 7, 40 and 41 can not be sides of a right triangle. The lengths 12, 16, and 20 can be sides of a right triangle.

Explanation:

for first part of statement

The lengths 7, 40 and 41 can not be sides of a right triangle.

If the square of long side is equal to the sum of square of other two sides

then the given length can be sides of a right triangle.

Check the given length by Pythagoras Theorem.

`c^(2) =a^(2) +b^(2)`----------(1)

Let
`c=41` and
`a = 7` and
`b=40`

Put all the value in equation 1.

`41^(2) =7^(2) +40^(2)`

`1681=49+1600`

`1681=1649`

Therefore, the square of long side is not equal to the sum of square of other two sides, So given lengths 7, 40 and 41 can not be sides of a right triangle.

for second part of statement.

The lengths 12, 16, and 20 can be sides of a right triangle.

Check the given length by Pythagoras Theorem.

Let
`c=20` and
`a = 12` and
`b=16`

`20^(2) =12^(2) +16^(2)`

`400=144+256`

`400=400`

Therefore, the square of long side is equal to the sum of square of other two sides, So given the lengths 12, 16, and 20 can be sides of a right triangle.

Therefore, The lengths 7, 40 and 41 can not be sides of a right triangle. The lengths 12, 16, and 20 can be sides of a right triangle.