Chapter 4.5, Problem 3STP

For Exercises $1-5,$ choose the correct letter.

Which function rule can be used to represent the area of a triangle with a base b 8 in. longer than twice the height $h$ in terms of the height?

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

C. $A=h^2+4h$

B. $A=\frac{1}{2}h(h+8)$

D. $A=\frac{1}{2}(2h)(h+8)$

To determine

To write the function rule that represents the area of the given triangle.

Answer to Problem 3STP

Function rule is $A=h^2+4h$ and option C is correct.

Explanation of Solution

Given:

The base b of the triangle is 8 inches longer than twice the height h.

Calculation:

Given,

  $b=2h+8$

Therefore the area of the triangle is,

  $\begin{array}{l}A=\frac{1}{2}\cdot b\cdot h\\ \Rightarrow A=\frac{1}{2}\cdot \left(2h+8\right)\cdot h\\ \Rightarrow A=\frac{1}{2}\cdot 2\left(h+4\right)\cdot h\\ \Rightarrow A=h\left(h+4\right)\\ \Rightarrow A=h^2+4h\end{array}$

Hence option C is correct.