Question

Can the set of lengths be the side lengths of a right triangle?

7ft, 12ft, 17 ft
A. Yes
B. No
C. Not enough information to answer the question

Answer 1

Answer: Hello there!

We know that in a right triangle, the sum of the squares of the cathetus is equal to the square of the hypotenuse.

the smaller sides given are:

7ft and 12ft, and the longest is 17ft

so if this triangle is a right triangle, we should have that:

7^2 + 12^2 = 17^2

17^2 = 289

7^2 + 12^2 = 193

The terms are different, which means that this is not a right triangle, then the correct answer is B.

Answer 2

B. No.

Explanation:

We have been given 3 side lengths 7 ft, 12 ft, 17 ft. We are asked to determine, whether the given set of lengths can form a right triangle or not.

We will use Pythagoras theorem to solve our given problem, which states that the square of hypotenuse of a right triangle is equal to the sum of squares of two legs of right triangle.

`17^2=12^2+7^2`

`289=144+49`

`289>193`

Since the sum of squares of both legs is less than square of hypotenuse, therefore, the given set of lengths can not be the side lengths of a right triangle.