High School

Muna hace un dibujo a escala de un geco. El geco mide [tex]\frac{1}{2}[/tex] pulgada de ancho y 5 pulgadas de largo.

a. Muna decide que su dibujo del geco mida 1 pulgada de ancho. ¿Cuál será la longitud del dibujo? Muestra tu trabajo.

b. Comprueba tu respuesta al problema 3a. Muestra tu trabajo.

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.