Problem
Yoko is making a small sign in the shape of a triangle for her store. She wants the base length of the triangle to be 4 inches. The area of the sign must be at most 12 square inches. (Yoko doesn't want to buy more material.) Write an inequality that describes the possible heights (in inches) of the triangle. Use h for the height of the triangular sign.
Solution
For this case the base needs to be b= 4
The maximum are needs to be A= 12
And we know that the area of the triangle is given by:
A= (b*h)/2
But we know that the area needs to be at most 12 square inches
A = 4h/2 <=12
And then we can solve for h and we got:
2h <= 12
h <= 6
So then we can conclude that the height needs to be lower or equal than 6