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.
