Question

The sum of the base and height of a triangle is 14 cm. Which of the following equations could be used to find the maximum area of the triangle?
A) A = 0.5x^2 - 15x

B) A = -0.5x^2 + 7x

C) A = -x^2 + 10x

D) A = x^2 - 10x

Answer 1

Answer:

B

Step-by-step explanation:

Let the base of the triangle be b and the height be h.

The sum of the base and height is 14. Thus:

$b+h=14$

Recall that the area of a triangle is given by:

$\displaystyle A=\frac{1}{2}bh$

From the first equation, solve for either variable:

$h=14-b$

Substitute:

$\displaystyle A=\frac{1}{2}b(14-b)$

Distribute:

$\displaystyle A=\frac{1}{2}(14b-b^2)$

Distribute:

$\displaystyle A=-0.5b^2+7b$

Let b = x. Hence:

$A=-0.5x^2+7x$

Therefore, our answer is B.