Question

You want to put up a fence that encloses a triangular region with an area greater than or equal to 60 square feet. What is the least possible value of c? Explain.

Answer 1

Hello there. To solve this question, we'll need to remember some properties about triangles.

First, the area of a right triangle as in the following drawing:

Can be calculated by the formula:

$A=\frac{a\cdot b}{2}$

If the area of the enclosed triangular region is greater than or equal to 60, we have the following inequality;

$A\ge60$

Now, using the lengths of the sides of the triangle, we'll have:

$A=\frac{c\cdot12}{2}=6c$

Therefore

$6c\ge60$

Divide both sides of the inequality by a factor of 6

$c\ge10$

The least possible value of c is 10 ft.