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Answer :
We begin by noting the actual dimensions of the gecko:
[tex]$$
\text{Actual width} = \frac{1}{2} \text{ inch}, \quad \text{Actual length} = 5 \text{ inches}.
$$[/tex]
(a) Calculating the drawing's length:
Since the drawing's width is set to be 1 inch, we first determine the scale factor by comparing the drawing's width to the actual width:
[tex]$$
\text{Scale factor} = \frac{\text{Drawing width}}{\text{Actual width}} = \frac{1}{\frac{1}{2}} = 2.
$$[/tex]
The drawing’s length is then found by multiplying the actual length by this scale factor:
[tex]$$
\text{Drawing length} = 5 \times 2 = 10 \text{ inches}.
$$[/tex]
(b) Verification of the answer:
To verify that the drawing is indeed to scale, we check the proportion between the drawing’s length and the gecko's actual length:
[tex]$$
\frac{\text{Drawing length}}{\text{Actual length}} = \frac{10}{5} = 2.
$$[/tex]
Similarly, we already computed the width ratio:
[tex]$$
\frac{\text{Drawing width}}{\text{Actual width}} = \frac{1}{\frac{1}{2}} = 2.
$$[/tex]
Since both ratios are equal to 2, the drawing maintains the same scale in both dimensions, confirming that the drawing's length is correctly calculated.
Final Answer:
a. The length of the drawing is [tex]$10$[/tex] inches.
b. Verification: The ratios [tex]$\frac{1}{\frac{1}{2}} = 2$[/tex] and [tex]$\frac{10}{5} = 2$[/tex] confirm the drawing is to scale.
[tex]$$
\text{Actual width} = \frac{1}{2} \text{ inch}, \quad \text{Actual length} = 5 \text{ inches}.
$$[/tex]
(a) Calculating the drawing's length:
Since the drawing's width is set to be 1 inch, we first determine the scale factor by comparing the drawing's width to the actual width:
[tex]$$
\text{Scale factor} = \frac{\text{Drawing width}}{\text{Actual width}} = \frac{1}{\frac{1}{2}} = 2.
$$[/tex]
The drawing’s length is then found by multiplying the actual length by this scale factor:
[tex]$$
\text{Drawing length} = 5 \times 2 = 10 \text{ inches}.
$$[/tex]
(b) Verification of the answer:
To verify that the drawing is indeed to scale, we check the proportion between the drawing’s length and the gecko's actual length:
[tex]$$
\frac{\text{Drawing length}}{\text{Actual length}} = \frac{10}{5} = 2.
$$[/tex]
Similarly, we already computed the width ratio:
[tex]$$
\frac{\text{Drawing width}}{\text{Actual width}} = \frac{1}{\frac{1}{2}} = 2.
$$[/tex]
Since both ratios are equal to 2, the drawing maintains the same scale in both dimensions, confirming that the drawing's length is correctly calculated.
Final Answer:
a. The length of the drawing is [tex]$10$[/tex] inches.
b. Verification: The ratios [tex]$\frac{1}{\frac{1}{2}} = 2$[/tex] and [tex]$\frac{10}{5} = 2$[/tex] confirm the drawing is to scale.
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