Which dimensions can create only one unique triangle?
three angles measuring 25 degrees, 65 degrees, and 90 degrees
three angles measuring 50 degrees, 50 degrees, and 50 degrees
three sides measuring 5 in., 12 in., and 14 in.
three sides measuring 4 ft, 8 ft, and 14 ft

Three sides measuring 5 in., 12 in., and 14 in.

First of all, you need to know some facts about every triangle:

FIRST FACT:

If two sides of a triangle are , then the third side must be less than . Why? because if its length is exactly , then you can't build up a triangle, but you'll have a line segment. In other words:

SECOND FACT:

The internal angles of any triangle add up to 180°. So if ∠A, ∠B and ∠C are the internal angles of a triangle, then:

__________________________

So let's analyze each case:

The sum is greater than 180 degrees, so these angles can't form a triangle

The sum is less than 180 degrees, so these angles can't form a triangle

The inequalities are true, so these sides form a triangle.

Case 4: Three sides measuring 4 ft, 8 ft, and 14 ft

Since the third inequality is not true, then we can't form a triangle with these sides.

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1