Answer
See the explanation
Work Step by Step
$\textbf{Part (a)}$
The area formula for a parallelogram is: $$A=bh\tag{1},$$ where:
• $A$ is the area,
• $b$ is the base,
• $h$ is the height.
$\textbf{Part (b)}$
The problem gives:
• $A = 30\text{ inch}^2$
• $h= 5\text{ inch}$
Substitute these values into equation $(1)$: $$30=b\cdot 5.$$ Solve for $b$.
$1.$ Divide both sides by $5$: $$\frac{30}{5}=\frac{b\cdot 5}{5}.$$ $2.$ Simplify $$6=b.$$
So, the base is $b=6\text{ inch}$.
$\textbf{Part (c)}$
Start with formula $(1)$.
Solve for $b$:
$1.$ Divide both sides by $h$: $$\frac{A}{h}=b.$$ $2.$ Rearrange the formula: $$b=\frac{A}{h}.$$ Now substitute the given values ($A$, $h$): $$b=\frac{30}{5}.$$ Simplify: $$b=6.$$
$\textbf{Part (d)}$
Similarities:
• Both methods use the formula $(1)$ and algebraic steps to solve for $b$.
• Both yield the same result: $6\text{ inch}$.
Differences:
• In part (b), substitution of values ($A$ and $h$) was done first, followed by solving for $b$.
• In part (c), the formula was rearranged to solve for $b$ first and then values were substituted.
