Question

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

7ft, 12ft, 17 ft

Answer 1

No

Explanation:

For a right triangle, a^2+b^2=c^2 EVERY time.

a and b are always smaller than c, so 7 and 12 are a and b, and 17 is c:

7^2+12^2 ?= 17^2

49+144 ?= 289

193 != 289

Therefore, these can't be the set of lengths for a right triangle

Answer 2

These set of lengths cannot be the side lengths of a right angled triangle.

Explanation:

Pythagoras Theorem is always followed by a right angled triangle. According to which the sum of squares of the two shorter legs is equal to the square of the longest leg.

`a^2=b^2+c^2`

So here, 17 is the longest leg and 7 and 12 the shorter ones.

Applying Pythagoras Theorem to these lengths to find out.

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

`289\\eq 193`

Therefore, these set of lengths cannot be the side lengths of a right angled triangle.