Question

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?

Answer 1

Answer with explanation:

Let Base =x in.

Height of triangle = (2 x +4) in.

Area of triangle ≤ 168 in.²

Area of Right Triangle

`=(1)/(2) * \text{Base} * \text{Height}\\\\=(1)/(2) * x * (2 x+4)`

→→The inequality that can be used to find the possible lengths, x, of the base of the triangle is:

`=(1)/(2)* x * (2 x+4)\leq 168\\\\\rightarrow x* (x+2)\leq 168\\\\\rightarrow x^2+2 x-168\leq 0`

Answer 2

To get the possible inequality for the above information will be given as follows;
suppose the base of the triangle is x;
height=2x-4
The area is no more than 168 in^2
Therefore, the area can be expressed as follows;
Area=1/2*base*height
1/2*x*(2x-4)≤168
x^2-4x≤168
the answer is x^2-4x≤168