Question

Which set of line segments could create a right triangle? A. 24, 30, 35 B. 12, 18 , 30 C. 18, 24, 30 D. 18, 24, 35

Answer 1

To be able to determine if the given line segments could create a right triangle, the following condition must be met:

$\text{ (Largest number)}^2\text{ = (Smallest number)}^2\text{ + (Second largest number)}^2\text{ }$

Let's check each of the given sets:

A.) 24, 30, 35 : The largest number is 35 and the rest are 24 and 30.

We get,

$\text{ (Largest number)}^2\text{ = (Smallest number)}^2\text{ + (Second largest number)}^2\text{ }$$\text{ 35}^2=24^2+30^2$$\begin{gathered} \text{ 1,225 = 576 + 900} \\ \text{ 1,225 }\ne\text{ 1,}476 \end{gathered}$

Therefore, the set: 24, 30 and 35 couldn't create a right triangle.

B.) 12, 18, 30 : The largest number is 30 and the rest are 12 and 18.

We get,

$\begin{gathered} \text{ 30}^2=12^2+18^2 \\ 900\text{ = 144 + 324} \\ 900\text{ }\ne\text{ 468} \end{gathered}$

Therefore, the set: 12, 18, and 30 couldn't create a right triangle.

C.) 18, 24, 30 : The largest number is 30 and the rest are 18 and 24.

We get,

$\begin{gathered} \text{ 30}^2=18^2+24^2 \\ 900\text{ = 324 + 576} \\ \text{ 900 = 900} \end{gathered}$

Therefore, the set: 8, 24, and 30 could create a right triangle.

The answer is letter C.