Question 1 • Advanced Algebra: Concepts and Connections
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 greater 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 less than or equal to 168
Explanation
If the base is x inches, the height is 2x + 4 inches. The triangle’s area is ½ × base × height, so ½x(2x + 4) = x(x + 2). Since the area is no more than 168 square inches, the inequality is x(x + 2) ≤ 168, which is choice B.
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