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

Correct option: B

When we say a is no more than b, we express this in a mathematical language as follows:

In this inequality, we know that the area of the triangle is no more than 168 in². In other words, if the area is named , then:

We also know that the height of a triangle is 4 inches greater than twice its base. Translating this in a mathematical language:

From geometry, we know that the area of a triangle is given by:

Matching (1), (2) and (3):

Since the length of the base of the triangle is , then

Finally, correct option is B.

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step-by-step explanation:

8+8+6+6