Question

Carlos is making a small sign in the shape of a triangle for her store. He wants the base length of the triangle to be 6 inches. The area of the sign must be more than 15 square inches. (The sign has to be seen from the sidewalk.) Write an inequality that describes the possible heights (in inches) of the triangle.

Use h for the height of the triangular sign.

Answer 1

Inequality:
`(1)/(2)(6)h>15in^(2)`

Solve for 'h': h > 5 in.

Explanation:

The formula for the area of a triangle is: area =
`(1)/(2)bh`, where 'b'=the length of the base and 'h' = the height. Since the area of the sign must be more than 15 in², the inequality must be '> 15 in²'.

Using the formula for area and the given values, we can set up the following inequality:

`(1)/(2)(6)h>15in^(2)`

Solving for 'h', we can first multiply both sides by
`(2)/(1)`:

`(2)/(1)(1)/(2)(6)h>15(2)/(1)`

Divide both sides by 6: 6h/6 > 30/6

Solve for h: h > 5in