Question

the height of a triangle is 4 in. greater than twice its base. the area of the triangle is no more. which inequality can be used to find the possible lengths, x, of the base of the triangle?
○ x(x + 2)≥188
○ x(x + 2)≤188
○ \frac{1}{2}x(x + 4)≤188
○ \frac{1}{2}x(x + 4)≥188

Explanation:

Step1: Define base and height

Let base be $x$, height $h = 2x + 4$.

Step2: Write area formula

Area $A=\frac{1}{2}\times base\times height=\frac{1}{2}x(2x + 4)=x(x + 2)$.

Step3: Set up inequality

Since area is no more than 188, $x(x + 2)\leq188$.

Answer:

B. $x(x + 2)\leq188$