Chapter 8.1, Problem 46IP

To determine

Equation and complete the table of values

Answer to Problem 46IP

The table is

Area(A)	15	15	15	15	15
Base(b)	1	2	3	4	5
Height(h) $h=\frac{2A}{b}$	30	15	10	7.5	6

Explanation of Solution

Given information:

The formula for finding the area of a triangle is $A=\frac{1}{2}bh$

  

Concept used:

Area of triangle $A=\frac{1}{2}bh$

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.
• Left distributive property: $a\left(b+c\right)=a\cdot b+a\cdot c$

Calculation:

In order to complete the table we put the values of b and A in equation $A=\frac{1}{2}bh$ as shown below

The equation is simplified as below

  $\begin{array}{c}A=\frac{1}{2}bh\\ \frac{2A}{b}=h\\ \Rightarrow h=\frac{2A}{b}\end{array}$

  $\begin{array}{c}A=15\text{and}b=1\\ h=\frac{2A}{b}\\ =\frac{2\cdot 15}{1}\\ h=30\\ A=15andb=2\\ h=\frac{2A}{b}\\ =\frac{2\cdot 15}{2}\\ =\frac{30}{2}\\ h=15\\ A=15andb=3\\ h=\frac{2A}{b}\\ =\frac{2\cdot 15}{3}\\ =\frac{30}{3}\\ h=10\\ A=15andb=4\\ h=\frac{2A}{b}\\ =\frac{2\cdot 15}{4}\\ =\frac{30}{4}\\ h=7.5\\ A=15andb=5\\ h=\frac{2A}{b}\\ =\frac{2\cdot 15}{5}\\ =\frac{30}{5}\\ h=6\end{array}$

Thus, the table is below

Area(A)	15	15	15	15	15
Base(b)	1	2	3	4	5
Height(h) $h=\frac{2A}{b}$	30	15	10	7.5	6