Question

Alan is making a small sign in the shape of a triangle for his store. He wants the height of the triangle to be 4 inches. The area of the sign must be less than 18 square inches. Write an inequality that describes the possible base length of the triangle.

Answer 1

`b<9`

Explanation:

We have been given that Alan is making a small sign in the shape of a triangle for his store. He wants the height of the triangle to be 4 inches. The area of the sign must be less than 18 square inches. We are asked to write an inequality that describes the possible base length of the triangle.

We will use area of rectangle formula to solve our given problem.

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

A = Area of triangle,

b = Base length,

h = Height of triangle.

As area must be less than 18 square inches, so we can represent this information in an inequality as:

`18>(1)/(2)b(4)`

`(1)/(2)b(4)<18`

`2b<18`

`(2b)/(2)<(18)/(2)`

`b<9`

Therefore, the length of he base should be less than 9 inches.

Answer 2

`b < 9`

Explanation:

We are given the following in the question:

Height of triangle,h = 4 inches

Area of triangle =

`A = (1)/(2)* b* h`

where b is the base of the triangle and h is the height of the triangle.

The area of the triangular sign must be less than 18 square inches.

Thus, we can write the inequality:

`A< 18\\\\\Rightarrow (1)/(2)* b * h < 18\\\\\Rightarrow b < (18* 2)/(4)\\\\\Rightarrow b < 9`

The above inequality is the required inequality that describes the possible base length of the triangular sign.