Question

Neil wants to join three pieces of metal to form a right triangle which of the following lengths could he use

A.) 4,4 and 8 feet B.) 7.5, 10 and 12.5 feet C.) 9, 11 and 23 feet D.) 6, 12.5 and 96 feet

Answer 1

Option B: 7.5, 10 and 12.5 feet forms a right triangle

Step-by-step explanation:

Given that neil wants to join three pieces of metal to form a right triangle.

We need to determine the set that forms a right triangle.

Since, we know that the hypotenuse of the triangle is the largest measurement in the triangle.

Thus, let us assume that the largest measurement in the given set is the hypotenuse of the triangle.

Option A: 4,4 and 8 feet

Using the Pythagorean theorem, we have,

`8^2=4^2+4^2`

`64=16+16`

`64\\eq 32`

Since, both sides of the equation are not equal, then the set 4,4 and 8 feet does not forms a right triangle.

Hence, Option A is not the correct answer.

Option B: 7.5, 10 and 12.5 feet

Using the Pythagorean theorem, we have,

`12.5^2=7.5^2+10^2`

`156.25=56.25+100`

`156.25=156.25`

Since, the both sides of the equation are equal, then the set 7.5, 10 and 12.5 feet forms a right triangle.

Hence, Option B is the correct answer.

Option C: 9, 11 and 23 feet

Using the Pythagorean theorem, we have,

`23^2=9^2+11^2`

`529=81+121`

`529\\eq 202`

Since, both sides of the equation are not equal, then the set 9, 11 and 23 feet does not forms a right triangle.

Hence, Option C is not the correct answer.

Option D: 6, 12.5 and 96 feet

Using the Pythagorean theorem, we have,

`96^2=6^2+12.5^2`

`9216=36+156.25`

`9216\\eq 192.25`

Since, both sides of the equation are not equal, then the set 6, 12.5 and 96 feet does not forms a right triangle.

Hence, Option D is not the correct answer.