Question

Rita is making a small sign in the shape of a triangle. She wants the base length of the triangle to be 4 inches. The area of the sign must be at least 16 square inches. Write an inequality that describes the possible heights (in inches) of the triangle. Use h for height.

Answer 1

The value of h must be greater than or equal to 8 inches

The minimum value of h is 8 inches

Explanation:

Let

h ----> the possible heights (in inches) of the triangle

we know that

The area of triangle is equal to

`A=(1)/(2)bh`

where

b is the base length

h is the height

In this problem we have

`b=4\ in`

Remember that the word "at least" means "greater than or equal to"

so

`A\geq 16\ in^2`

The inequality that represent this problem is

`(1)/(2)bh\geq 16`

substitute the value of b

`(1)/(2)(4)h\geq 16`

`2h\geq 16`

`h\geq 8\ in`

The value of h must be greater than or equal to 8 inches

The minimum value of h is 8 inches