The height of a triangle is 4 in. greater than twice its base. The area of the triangle is no more than 168 in. squared Which inequality can be used to find the possible lengths, x , of the base of the triangle?
Answer
A
1 half x open paren x plus 4 close paren is less than or equal to 168
B
x times open paren x plus 2 close paren is less than or equal to 168
C
x times open paren x plus 2 close paren is greater than or equal to 168
D
1 half x open paren x plus 4 close paren is greater than or equal to 168
Explanation
The base is x inches, and the height is 4 more than twice the base, so the height is 2x + 4. The triangle’s area is one-half times base times height, giving ½x(2x + 4) ≤ 168. This simplifies to x(x + 2) ≤ 168, but that expression is not listed; choice A instead uses height x + 4 and is inconsistent with the wording. Therefore none of the choices is correct.
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