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The table shows the dimensions of four wedges.

Dimensions of Four Wedges
\begin{tabular}{|c|c|c|}
\hline
& \begin{tabular}{l}
Thickness at widest part \\
(in.)
\end{tabular}
& \begin{tabular}{l}
Slope \\
(in.)
\end{tabular} \\
\hline
[tex]$w$[/tex] & 2 & 5 \\
\hline
[tex]$x$[/tex] & 4 & 8 \\
\hline
[tex]$y$[/tex] & 3 & 9 \\
\hline
[tex]$z$[/tex] & 5 & 10 \\
\hline
\end{tabular}

Which wedge requires the least amount of force to do a job?

A. [tex]$w$[/tex]
B. [tex]$x$[/tex]
C. [tex]$y$[/tex]
D. [tex]$z$[/tex]



Answer :

GinnyAnswer
To determine which wedge requires the least amount of force to do a job, we need to compare the force for each wedge. The force for each wedge can be represented by the ratio of the thickness at the widest part to the slope. A smaller ratio indicates less force required.

Let's analyze each wedge one by one:

1. Wedge [tex]\( W \)[/tex]:
- Thickness: 2 inches
- Slope: 5 inches

Force [tex]\( = \frac{\text{Thickness}_W}{\text{Slope}_W} = \frac{2}{5} = 0.4 \)[/tex]

2. Wedge [tex]\( X \)[/tex]:
- Thickness: 4 inches
- Slope: 8 inches

Force [tex]\( = \frac{\text{Thickness}_X}{\text{Slope}_X} = \frac{4}{8} = 0.5 \)[/tex]

3. Wedge [tex]\( Y \)[/tex]:
- Thickness: 3 inches
- Slope: 9 inches

Force [tex]\( = \frac{\text{Thickness}_Y}{\text{Slope}_Y} = \frac{3}{9} = 0.33 \)[/tex]

4. Wedge [tex]\( Z \)[/tex]:
- Thickness: 5 inches
- Slope: 10 inches

Force [tex]\( = \frac{\text{Thickness}_Z}{\text{Slope}_Z} = \frac{5}{10} = 0.5 \)[/tex]

Now, let's compare the calculated forces:

- Force for [tex]\( W \)[/tex]: 0.4
- Force for [tex]\( X \)[/tex]: 0.5
- Force for [tex]\( Y \)[/tex]: 0.33
- Force for [tex]\( Z \)[/tex]: 0.5

The wedge that requires the least amount of force is the one with the smallest ratio. Comparing the values, [tex]\( W = 0.4 \)[/tex], [tex]\( X = 0.5 \)[/tex], [tex]\( Y = 0.33 \)[/tex], and [tex]\( Z = 0.5 \)[/tex]:

The smallest ratio is 0.33.

Therefore, Wedge [tex]\( Y \)[/tex] requires the least amount of force to do the job.

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