Question

the height of a triangle is 4 in. greater than twice its base. the area of the triangle is no more than 168 in². which inequality can be used to find the possible lengths, x, of the base of the triangle?
○ x(x + 2)≥168
○ x(x + 2)≤168
○ 1/2 x(x + 4)≤168
○ 1/2 x(x + 4)≥168

Explanation:

Answer:

Let the base of the triangle be \(x\) inches. The height \(h\) of the triangle is \(h = 2x + 4\) inches. The area formula for a triangle is \(A=\frac{1}{2}bh\), where \(b\) is the base and \(h\) is the height. Substituting \(b = x\) and \(h=2x + 4\) into the area - formula, we get \(A=\frac{1}{2}x(2x + 4)\). Since the area of the triangle is no more than \(168\) square inches, the inequality is \(\frac{1}{2}x(2x + 4)\leq168\), which simplifies to \(x(x + 2)\leq168\).
So the answer is \(x(x + 2)\leq168\)