Question

A triangle has side lengths measuring 2x + 2 ft, x + 3 ft, and n ft.

Which expression represents the possible values of n, in feet? Express your answer in simplest terms.

A. x – 1 < n < 3x + 5
B. n = 3x + 5
C. n = x – 1
D. 3x + 5 < n < x – 1

Answer 1

The answer is A. x-1,n,3x+5

Answer 2

The correct option is A. x – 1 < n < 3x + 5

Explanation:

In a triangle sum of any two sides is always greater than the third side.

Now, the sides of the triangle are given to be :

2x + 2, x + 3 , n

Now, first take 2x + 2 and x + 3 as two sides and the side of length n as third side.

By using the property that sum of two sides is always greater than the third side in a triangle.

⇒ 2x + 2 + x + 3 > n

⇒ 3x + 5 > n ......(1)

Now, take n and x + 3 as two sides and the side of length 2x + 2 as the third side of triangle.

So, by the property, we have :

n + x + 3 > 2x + 2

⇒ n > x - 1 ...........(2)

From both the equations (1) and (2) , We get :

x – 1 < n < 3x + 5

Therefore, The correct option is A. x – 1 < n < 3x + 5