Question

triangle abc is shown in the diagram. the lengths of the sides are in terms of the variable n, where n>4. Complete the inequality

Answer 1

Answer:

In the first box, B; in the second box, A; and in the third box, C.

Step-by-step explanation:

The sides marked on the triangle would be ranked in order from least to greatest as

n+3, 2n, 3n-2.

This is because for numbers greater than 3 (we are told that n is greater than or equal to 4), adding 3 to a number is less than multiplying it by 2.

Multiplying a number by 2 is less than multiplying a number by 3 then subtracting 2.

To test, use 4:

n+3 = 4+3 = 7; 2n = 2(4) = 8; 3n-2 = 3(4)-2 = 12-2 = 10.

The angles associated with these sides are across from them.  The angle across from the side marked n+3, AC, is angle B.  The angle across from the side marked 2n, BC, is angle A.  The angle across from the side marked 3n-2, AB, is angle C.

Answer 2

If n>4, then n+3<2n<3n-2 (n+3<2n is true because this unequality is equivalent to 3<n and 2n<3n-2 is also true because this unequality is equivalent to 2<n). Hence, the side AC is the smallest one and the side AB is the biggest one.
The largest side is opposite the largest angle, the medium side is opposite the medium angle and the smallest side is opposite the smallest angle.

Then, m∠B<m∠A<m∠C.
Answer: m∠B<m∠A<m∠C.