In earlier lessons, you learned about proportions and how to set up them up and solve them. In this lesson, yous will larn to utilize scale drawings and scale models to solve problems. Ascale cartoon shows an object with its measurements in proportion to the actual measurements of the object. They are similar (proportional) to the actual object. Thescale is a ratio that compares the measurement used in a scale drawing with the actual measurements. Scales do not have to be in the same units. The scale factor is the constant of proportionality. When the units are the same, calibration gene tells you how many times larger or smaller the bodily object is compared to the measurements in the drawings or models.

Scale drawings are typically used when objects are too small-scale or likewise large to be drawn to their actual size. Maps, firm plans, and biology cell drawings are examples of items that employ calibration drawings. When using a model, calibration factor is e'er the ratio of the model's dimensions to the actual object'due south dimensions.

Investigate

statue of liberty.png

The Statue of Freedom is 1824 inches tall. Jamie bought a model in the souvenir shop that was 8 inches tall. How tin can we observe out what calibration factor was used to build the model?

Strategy

Nosotros know that the measurements of the statue and the model are proportional, so nosotros can start by writing this as a proportion: day 111.1 .

Solution

We simplify the fraction by dividing 8 into both the numerator and the denominator to go day 111.2 . This means that the statue is 228 times taller than the model, or we reduced the size of the statue by 228 to become the model.

A map is a blazon of scale cartoon. You can apply the scale on a map to discover real-world distances, or you lot tin apply the scale to make an accurate map.

Investigate

day 111.3

What is the actual distance betwixt the pond and the cabins?

Strategy

Write the scale as a ratio: day 111.4

Side by side, write a proportion and let x represent the actual altitude. day 111.5

Solve the proportion:

day 111.6

Solution

The actual distance between the cabins and the pond is 48 yards.

Scale Drawings are often used to build houses.

Investigate

day 111.7

Patty'southward father made her a dollhouse which was designed subsequently the blueprint of their home. The blueprint is xx inches wide by 42 inches long. The scale factor is day 111.8 . Find the size of the dollhouse.

Strategy

Think: day 111.9

Let'southward commencement with the width (w) and write a proportion

day 111.91

Permit the length be represented by l. Write a proportion.

day 111.92

Solution

The dollhouse will exist 60 inches wide and 126 inches long.

Hither are some videos to assistance y'all along. Try to reply the questions along with the video, just like I hope y'all did with the questions above.

Video one – scale drawings

Video two – give-and-take trouble

Practice

  1. The calibration on a map is five centimeters = 75 kilometers. Two lakes on the map are located 8.1 cm apart. What is the bodily distance between the two lakes?
  2. The calibration of a map is one and ane quarter inches = 50 miles. On that map, two cities are iv and 1 half inches autonomously. What is the actual distance between the cities?
  3. Angela fabricated a scale drawing of her sleeping accommodation using a scale of 0.5 cm = 1 meter. The actual length of her bedroom is 5 meters. What is the length of Angela'southward bedroom on the scale drawing?
  4. The Watson family went on holiday. On the kickoff mean solar day, they drove a distance shown as 4 inches on a map. The actual distance that they drove was 240 miles. What was the scale of the map?

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