The height of a triangle is 4 in. greater than twice its base. The area of the triangle is no more than 168 in.2. Which inequality can be used to find the possible lengths, x, of the base of the triangle?
1/2 bh <= 168
1/2 b(2b+4) <= 168
or, use x instead of b if you want.
Let's start by assuming that the length of the base of the triangle is x inches.
According to the given information, the height of the triangle is 4 inches greater than twice its base. Therefore, the height can be expressed as (2x + 4) inches.
The formula for finding the area of a triangle is given by:
Area = (1/2) * base * height
Substituting the values we have:
168 ≤ (1/2) * x * (2x + 4)
Simplifying the equation, we get:
168 ≤ x^2 + 2x
To find the possible lengths, x, of the base of the triangle, we can express this inequality as:
x^2 + 2x - 168 ≤ 0
To find the inequality that represents the possible lengths of the base of the triangle, we need to analyze the information given in the problem and define the relationships between the base, the height, and the area of the triangle.
Let's denote the base of the triangle as "x" (in inches).
According to the problem, the height of the triangle is 4 inches greater than twice its base. Therefore, we can express the height as 2x + 4 (in inches).
Now, let's calculate the area of the triangle. The formula for the area of a triangle is (1/2) x base x height. Substituting the values we have, the area becomes:
Area = (1/2) x x x (2x + 4)
Area = x^2 + 2x
The problem states that the area of the triangle is no more than 168 in^2. Therefore, we can write the inequality:
x^2 + 2x ≤ 168
This inequality represents the possible lengths of the base (x) that would satisfy the given conditions of the problem.