Question

A triangle has side lengths of n, n – 3, and 2(n − 2). If the perimeter of the triangle is at least 37 units, what is the value of n?

OA.

n> 11

OB

n> 8

O C.

n > 10. 5

OD

n > 7. 5

Answer 1

A. n ≥ 11

Explanation:

You have a triangle with sides (n), (n-3), and 2(n-2). Its perimeter is at least 37 units, and you want to know the value of n.

Perimeter

The perimeter is the sum of the side lengths:

P = (n) +(n -3) +2(n -2)

P = n + n -3 +2n -4

P = 4n -7

Constraint

The perimeter is at least 37, so we have ...

P ≥ 37

4n -7 ≥ 37

4n ≥ 44 . . . . . . . add 7

n ≥ 11 . . . . . . . divide by 4

The value of n is at least 11.