Question

Determine whether the given lengths can be sides of a right triangle. Which of the following are true statements. A.The lengths 7, 40 and 41 can not be sides of a right triangle. B.The lengths 12, 16, and 20 can not be sides of a right triangle. C.The lengths 7, 40 and 41 can not be sides of a right triangle.D.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.

Answer 1

Given sides 12, 16 and 20 can be the sides of right triangle.

Explanation:

Sides of right triangle always follow the Pythagoras theorem.

i.e
`(base)^2 + (Height)^2 = (Hypotenuse)^2`

For the given Lengths 7, 40 and 41

We need to check if

`7^2 + 40^2 =41^2 \\or\\ 7^2 + 40^2 \\eq41^2`

`Since \\7^2 + 40^2 = 1649\\and \\41^2 = 1681`

That means,
`\\ 7^2 + 40^2 \\eq 41^2`

hence 7,40 and 41 can not be the sides of right triangle.

Next,

Given sides 12,16 and 20.

Again follow the similar process used in the above problem.

`12^2 + 16^2 =400\\And \\20^2 = 400\\Since 12^2 + 16^2 = 20^2`

Therefore given sides 12,16 and 20 can be the sides of right triangle.