Question

solve the problems. 1 sara uses a scale of 1 cm : 12 m to draw a floor plan of a new store. she has to redraw the drawing so that it is larger for her presentation. could sara use the following scales? select yes or no for each scale. a. 1 cm : 8 m b. 1 cm : 20 m c. 2 cm : 24 m d. 3 cm : 15 m how long would a 12 - meter wall be on each scale?

Explanation:

Part 1: Determine if the scale makes the drawing larger

To make the drawing larger, the new scale should represent more meters per centimeter than the original scale (\(1\) cm : \(12\) m). A larger scale (in terms of the drawing size) means a smaller ratio of centimeters to meters (i.e., more meters per centimeter).

a. Scale: \(1\) cm : \(8\) m

The original scale is \(1\) cm : \(12\) m. The new scale has \(8\) m per cm, which is less than \(12\) m per cm. So this scale would make the drawing smaller, not larger. So answer is No.

b. Scale: \(1\) cm : \(20\) m

The new scale has \(20\) m per cm, which is more than \(12\) m per cm. So this scale would make the drawing larger. So answer is Yes.

c. Scale: \(2\) cm : \(24\) m

Simplify this scale: \(\frac{24\space m}{2\space cm}= 12\space m/cm\). This is the same as the original scale, so it doesn't make the drawing larger. So answer is No.

d. Scale: \(3\) cm : \(15\) m

Simplify this scale: \(\frac{15\space m}{3\space cm} = 5\space m/cm\). This is less than \(12\) m per cm, so it makes the drawing smaller. So answer is No.

Part 2: Length of 12 - meter wall on each scale

We use the formula: \(\text{Length on drawing (cm)}=\frac{\text{Actual length (m)}}{\text{Meters per centimeter in scale}}\)

a. Scale: \(1\) cm : \(8\) m

\(\text{Length}=\frac{12}{8} = 1.5\) cm

b. Scale: \(1\) cm : \(20\) m

\(\text{Length}=\frac{12}{20}=0.6\) cm

c. Scale: \(2\) cm : \(24\) m (or \(1\) cm : \(12\) m)

\(\text{Length}=\frac{12}{12} = 1\) cm

d. Scale: \(3\) cm : \(15\) m (or \(1\) cm : \(5\) m)

\(\text{Length}=\frac{12}{5}=2.4\) cm

Final Answers (for the "Yes/No" part):

a. \(\boxed{\text{No}}\)
b. \(\boxed{\text{Yes}}\)
c. \(\boxed{\text{No}}\)
d. \(\boxed{\text{No}}\)

(For the length part, if needed, the lengths are: a. \(1.5\) cm, b. \(0.6\) cm, c. \(1\) cm, d. \(2.4\) cm)

Answer:

Part 1: Determine if the scale makes the drawing larger

To make the drawing larger, the new scale should represent more meters per centimeter than the original scale (\(1\) cm : \(12\) m). A larger scale (in terms of the drawing size) means a smaller ratio of centimeters to meters (i.e., more meters per centimeter).

a. Scale: \(1\) cm : \(8\) m

The original scale is \(1\) cm : \(12\) m. The new scale has \(8\) m per cm, which is less than \(12\) m per cm. So this scale would make the drawing smaller, not larger. So answer is No.

b. Scale: \(1\) cm : \(20\) m

The new scale has \(20\) m per cm, which is more than \(12\) m per cm. So this scale would make the drawing larger. So answer is Yes.

c. Scale: \(2\) cm : \(24\) m

Simplify this scale: \(\frac{24\space m}{2\space cm}= 12\space m/cm\). This is the same as the original scale, so it doesn't make the drawing larger. So answer is No.

d. Scale: \(3\) cm : \(15\) m

Simplify this scale: \(\frac{15\space m}{3\space cm} = 5\space m/cm\). This is less than \(12\) m per cm, so it makes the drawing smaller. So answer is No.

Part 2: Length of 12 - meter wall on each scale

We use the formula: \(\text{Length on drawing (cm)}=\frac{\text{Actual length (m)}}{\text{Meters per centimeter in scale}}\)

a. Scale: \(1\) cm : \(8\) m

\(\text{Length}=\frac{12}{8} = 1.5\) cm

b. Scale: \(1\) cm : \(20\) m

\(\text{Length}=\frac{12}{20}=0.6\) cm

c. Scale: \(2\) cm : \(24\) m (or \(1\) cm : \(12\) m)

\(\text{Length}=\frac{12}{12} = 1\) cm

d. Scale: \(3\) cm : \(15\) m (or \(1\) cm : \(5\) m)

\(\text{Length}=\frac{12}{5}=2.4\) cm

Final Answers (for the "Yes/No" part):

a. \(\boxed{\text{No}}\)
b. \(\boxed{\text{Yes}}\)
c. \(\boxed{\text{No}}\)
d. \(\boxed{\text{No}}\)

(For the length part, if needed, the lengths are: a. \(1.5\) cm, b. \(0.6\) cm, c. \(1\) cm, d. \(2.4\) cm)