Question

1. capria is planning to fence a triangular plot of land. two of the sides of the plot measure 230 yards and 490 yards.

a. find the range for the measure of the third side of the triangular plot of land.
b. what are the maximum and minimum lengths of fencing capria will need?

Explanation:

Step1: Apply triangle inequality for min side

Let the third side be $x$. The sum of two sides must exceed the third: $490 - 230 < x$
<Expression>
$490 - 230 = 260$, so $x > 260$
</Expression>

Step2: Apply triangle inequality for max side

The third side must be less than the sum of the two given sides: $x < 230 + 490$
<Expression>
$230 + 490 = 720$, so $x < 720$
</Expression>

Step3: Calculate min fencing length

Minimum fencing is just above the sum of the two sides plus the smallest possible third side: $230 + 490 + 260$ (approaching this value)
<Expression>
$230 + 490 + 260 = 980$ yards (approaching, not including)
</Expression>

Step4: Calculate max fencing length

Maximum fencing is just below the sum of the two sides plus the largest possible third side: $230 + 490 + 720$ (approaching this value)
<Expression>
$230 + 490 + 720 = 1440$ yards (approaching, not including)
</Expression>

Answer:

a. The range for the third side is $260 < x < 720$ yards
b. Minimum fencing length: approaches 980 yards (greater than 980 yards); Maximum fencing length: approaches 1440 yards (less than 1440 yards)