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Clara is building a triangular garden. She wants the length of the longest side to be three more than twice as long as the length of the shortest side, and the third side will be twelve feet long.

What expression could she write to determine the perimeter of the triangle if s represents the length of the shortest side? (Recall that perimeter is the distance around a shape.)



What is the expression in simplified form?



What is the coefficient of the variable in the simplified expressio



Answer :

Answer:To help Clara determine the dimensions of her triangular garden, we can set up an equation based on her description. Let's denote the length of the shortest side as

x.

Step-by-step explanation:The longest side is described as three more than twice the length of the shortest side:

2

+

3

2x+3.

The third side will need to satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the remaining side.

Let's denote the third side's length as

y.

According to the triangle inequality theorem, the following must be true:

+

>

2

+

3

x+y>2x+3

+

(

2

+

3

)

>

x+(2x+3)>y

+

(

2

+

3

)

>

y+(2x+3)>x

From these inequalities, we can derive conditions for

x and

y. Would you like to proceed with solving these inequalities, or do you have a specific value for the third side

y in mind?

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