Scale Drawings Sec 5. 2-B pg. 284 - 290

Definitions SCALE DRAWINGS or SCALE MODELS are used to represent objects that are too large or too small to be drawn or built at actual size. The SCALE gives the ratio that compares the measurements of the drawing or model to the measurements of the real object. Scale 1 inch = 2 feet To find the height of the actual person, you solve a proportion. 1 𝑖𝑛𝑐ℎ 2 𝑓𝑒𝑒𝑡 = 3 𝑖𝑛𝑐ℎ𝑒𝑠 𝑥 𝑓𝑒𝑒𝑡 3 inches (1inch)(x feet) = (2 feet)(3 inches) (1 𝑖𝑛𝑐ℎ)(𝑥 𝑓𝑒𝑒𝑡) (1 𝑖𝑛𝑐ℎ) = (2 𝑓𝑒𝑒𝑡)(3 𝑖𝑛𝑐ℎ𝑒𝑠) 1 𝑖𝑛𝑐ℎ x = 6 feet

Another Example The distance on the drawing from Winston-Salem to Raleigh is 1.6 centimeters. Find the distance in kilometers using the scale 1 cm = 75 km. 1.6 cm 1 𝑐𝑚 75 𝑘𝑚 = 1.6 𝑐𝑚 𝑥 x = 120 km x = (1.6)(75)

Scale Factor A scale written as a ratio without units in simplest form is called the SCALE FACTOR. Find the scale factor of ½ inch = 3 feet. We need both numbers to be in the same units. 1foot = 12 inches, so 3 feet = (3)(12 inches) = 36 inches. Multiply top and bottom by 2 to eliminate the fraction in the numerator. 1 2 𝑖𝑛𝑐ℎ 3 𝑓𝑒𝑒𝑡 = 1 2 𝑖𝑛𝑐ℎ 36 𝑖𝑛𝑐ℎ𝑒𝑠 1 2 𝑖𝑛𝑐ℎ 36 𝑖𝑛𝑐ℎ𝑒𝑠 ∗ (2) (2) 1 72 Scale Factor

Solve this problem How tall is the bridge? How long is the bridge? 1 𝑐𝑚 10 𝑓𝑡 = 4.5 𝑐𝑚 𝑥 x = (4.5)(10) x = 45 feet 1 𝑐𝑚 10 𝑓𝑡 = 14 𝑐𝑚 𝑥 How long? x = (10) (14) x = 140 feet