Question

The height of a triangle is 4 inches 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?

A. x(x+2)=>168
B. x(x+2)=<168
C. 1/2x(x+4)=<168
D. 1/2x(x+4)=>168

Answer 1

To find the possible lengths of the base of the triangle, use the given information about the height and area, and solve the inequality.

Step-by-step explanation:

To find the possible lengths, x, of the base of the triangle, we can use the given information about the height and area of the triangle. Let's assume the base of the triangle is x inches. According to the problem, the height of the triangle is 4 inches greater than twice its base, so the height would be 2x + 4 inches. The area of the triangle is given by the formula 1/2 x base x height, which in this case would be 1/2 x x x (2x + 4). The inequality that represents the area of the triangle being no more than 168 in² is:

1/2 x x x (2x + 4) ≤ 168

This inequality represents the possible lengths, x, of the base of the triangle.

Answer 2

b = x - the base
h = 2x + 4 - the height

Formula of the area of the triangle:


`A_\Delta=(1)/(2)bh`

substitute:


`A_\Delta=(1)/(2)x(2x+4)=x\left((1)/(2)\cdot2x+(1)/(2)\cdot4\right)=x(x+2)`

Answer:
`B.\ x(x+2)\leq168`