Question

Write a function rule for the area A of a triangle whose base, b, is 2 cm less than seven times the height, h. What is the area of the triangle when the height is 14 cm?

Answer 1

Let h be the height of the triangle. With this the base may be represented as 7h - 2. The area of the triangle is half the product of its base and height. Therefore,
                                   A = (1/2)bh = (1/2)(7h - 2)h
Substitute to the equation the value of h, 
                                     A = (1/2)((7)(14 cm) - 2)(14 cm)
                                          A = 672 cm²

Answer 2

Answer:

$A(h)=\frac{7}{2}h^{2}-h(cm)$

The area of the triangle is $672cm^{2}$ when the height is 14 cm.

Step-by-step explanation:

We start by finding the function rule for the area A.

We know reading the exercise that ''The base b is 2 cm less than seven times the height h''

Let's turn this into an equation :

$b=7h-2cm$ (I)

The area of a triangle is $\frac{b.h}{2}$ (II)

Given that ''b'' is the base and ''h'' is the height.

Now we replace (I) in (II).

$A=\frac{b.h}{2}=\frac{(7h-2cm).h}{2}=\frac{7h^{2}-2h(cm)}{2}=\frac{7}{2}h^{2}-h(cm)$

The area A is a function of the variable ''h''

$A(h)=\frac{7}{2}h^{2}-h(cm)$

That is the function rule for the area A.

To find the area when the height is 14 cm we replace in the function rule h by 14 cm ⇒

$A(14cm)=\frac{7}{2}(14cm)^{2}-14cm(cm)=686cm^{2}-14cm^{2}=672cm^{2}$

The area of the triangle is $672cm^{2}$ when the height is 14 cm.