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,…

Question

asked Dec 5, 2020 96.3k views

1 Answer

John Lord · Answer 1 · 2020-12-08T20:33:24+0000

Correct option: B

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

$a\leq b$

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:

$\mathbf{(1)} \ A\leq 168$

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

$\mathbf{(2)} \ h=2b+4 \\ \\ h:height \ of \ the \ triangle \\ \\ b:base \ of \ the \ triangle$

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

$\mathbf{(3)} \ A=(bh)/(2)$

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

$(bh)/(2)\leq 168$

Since the length of the base of the triangle is
, then
b=x

$(x(2x+4))/(2)\leq 168 \\ \\ Common \ factor \ 2: \\ \\ (2x(x+2))/(2)\leq 168 \\ \\ \boxed{x(x+2)\leq 168}$

Finally, correct option is B.