Answer
$D$
Work Step by Step
Let's look at each of the options separately.
Option A: Using the Triangle Inequality Theorem, we need to see if the sum of each of the combinations of two sides is greater than the other side:
$7 + 10 > 25$ --> This statement is false.
$10 + 25 > 7$ --> This statement is true.
$7 + 25 > 10$ --> This statement is true.
A triangle cannot have these lengths for its sides because two of the sides added together are not greater than the third side.
Option B: Using the Triangle Inequality Theorem, we need to see if the sum of each of the combinations of two sides is greater than the other side:
$4 + 6 > 10$ --> This statement is false.
$6 + 10 > 4$ --> This statement is true.
$10 + 4 > 6$ --> This statement is true.
A triangle cannot have these lengths for its sides because two of the sides added together are not greater than the third side.
Option C: Using the Triangle Inequality Theorem, we need to see if the sum of each of the combinations of two sides is greater than the other side:
$1 + 2 > 4$ --> This statement is false.
$2 + 4 > 1$ --> This statement is true.
$1 + 4 > 2$ --> This statement is true.
A triangle cannot have these lengths for its sides because two of the sides added together are not greater than the third side.
Option D: Using the Triangle Inequality Theorem, we need to see if the sum of each of the combinations of two sides is greater than the other side:
$3 + 5 > 7$ --> This statement is true.
$5 + 7 > 3$ --> This statement is true.
$3 + 7 > 5$ --> This statement is true.
These lengths can form a triangle because the sum of two sides is always greater than the third side.
