Scale for Drawing and Models

Using scale combines 2 concepts we’ve used before – similar figures and proportions.

A scale drawing is a two-dimensional drawing (or map) that accurately represents an object. A scale model is a three-dimensional model that accurately represents a solid object.

The scale drawing or modelis mathematically similar to the actual drawing or object.

A scale gives the ratio of the dimensions in the drawing (or model) to the dimensions of the actual object. All dimensions are reduced or enlarged using the same scale. Scales can use the same units or different units.

A scale factor describes how much a figure is enlarged or reduced. A scale factor can be expressed as a decimal, fraction or percent. A 10% increase is a scale factor of 1.1 and 10% decrease is a scale factor of 0.9.

Using scale factor to find missing dimensions:

A picture 4 in. tall and 9 in. wide is to be scaled to 2.5 in. tall to be displayed on a Web page. How wide should the picture be on the Web page for the two pictures to be similar?

To find the scale factor, divide the known height of the scaled picture by the corresponding height of the original picture.

0.625 is the scale factor

Then multiply the width of the original picture by the scale factor.

The picture should be 5.625 in. wide.

Using a proportion to find missing dimensions:

A company’s logo is in the shape of an isosceles triangle with two sides that are each 2.4 in. long and one side that is 1.8 in. long. On a billboard, the triangle in the logo has two sides that are each 8 ft. long. What is the length of the third side of the triangle on the billboard?

Set up a proportion.

The third side of the triangle is 6 ft. long.

Using proportions to find unknown scales or lengths:

The length of an object on a scale drawing is 5 cm, and its actual length is 15 m. the scale is

1 cm: ____ m. What is the scale?

Set up a proportion using

The scale is 1 cm:3 m.

The length of an object on a scale drawing is 3.5 in. The scale is 1 in:12 ft. What is the actual length of the object?

Pre-AlgebraName ______

Using Scales

Solve.

  1. A 10 ft fence is 8 in long on a scale drawing. What is the scale?
  1. Using a scale of 2 cm: 9 m, how long is an object that is 4.5 cm long on a drawing?
  1. A rectangular house is 32 ft wide and 68 ft long. On a blueprint, the width is 8 in. Find the length on the blueprint.
  1. Karen enlarged a 3 in wide by 5 in tall photo into a poster. If the poster is 2.25 ft wide, how tall is it?
  1. Frank scans a document that is 8.5 in wide by 11 in long into his computer. If he scales the length down to 7 in, about how wide should the similar document be? (round to the tenths place)
  1. The height of a person on a scale drawing is 4.5 in. The scale is 1:16. What is the actual height of the person?
  1. Using a scale of 2 cm = 25 m, find the length of an item on a scale drawing with an actual length of 475 m?
  1. What is the scale of a drawing in which a 9 ft wall is 6 cm long?