Question

The area of the triangle is less than 18 square inches. Find the possible

values of a by writing and solving an inequality.
Area of a triangle = (base height)
a
6 in



⚠️HELP IM FAILING MATH⚠️

Answer 1

0 < a < 6

or

(0, 6) in interval notation

Explanation:

The area of the triangle is

`Area \;A = (1)/(2)(base \cdot height)\\`

We are given base = 6 in, height = a and area A < 18 in²

Using the formula for area we get

`A = (1/2)(6 \cdot a) = 3a`

We know this area is < 18

So 3a < 18

Dividing both sides by 3 gives us
3a/3 < 18/3

a < 6

So height a must be less than 6 inches.
Height cannot be 0 so the lower bound on height is

a > 0

Putting these together we get the rang of a as
0 < a < 6

In Interval notation this is written as (0, 6)

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