Question

Jane is making a pennant in the shape of a triangle for her senior class photo. She wants the base length of this triangle to be inches. The area of the pennant must be at most square inches. (Jane doesn't want to buy more materials.) Write an inequality that describes the possible heights (in inches) of the triangle.

Use for the height of the triangular pennant.

Answer 1

h ≤ 6

Step-by-step:

Let h be the height of the triangular pennant in inches.

The formula for the area of a triangle is:

A = 1/2 * base * height

We know that the base of the triangle is 10 inches, so we can substitute this value into the formula:

A = 1/2 * 10 * h

Simplifying this equation, we get:

A = 5h

We also know that the area of the pennant must be at most 30 square inches. So we can write:

A ≤ 30

Substituting the formula for the area, we get:

5h ≤ 30

Dividing both sides by 5, we get:

h ≤ 6

Therefore, the possible heights of the triangle must be at most 6 inches in order for the area of the pennant to be at most 30 square inches.

The inequality that describes the possible heights of the triangle is:

h ≤ 6