7.G.1 Scale Drawings Review

Scale drawings When trying to find the scale factor you must remember that it must be written as a proportion in one of two forms Model : Actual or 𝑚𝑜𝑑𝑒𝑙 𝑎𝑐𝑡𝑢𝑎𝑙 Find the scale factor for the following Actual Model Length of Car Hood 3 ft 1in 𝑀𝑜𝑑𝑒𝑙: 1 𝑖𝑛 𝐴𝑐𝑡𝑢𝑎𝑙: 3 𝑓𝑡 𝑜𝑟 1 𝑖𝑛 :3 𝑓𝑡 NEVER DIVIDE IT OUT!!! IT MUST BE WRITTEN AS A PROPORTION OR RATIO!

When finding equivalent scale factors A map of Sweden shows that 5cm equals 3 km. If the distance between Knivsta and Stockholm is 6 cm on the map how many km is it? When finding equivalent scale factors you must remember that label need to match!!! The numerator labels need to match and the denominator labels need to match. You also have to make sure that you label your final answer correctly. 5 𝑐𝑚 3 𝑘𝑚 = 6 𝑐𝑚 𝑥 𝑘𝑚 Then you cross multiply and solve for x by dividing. 5 𝑐𝑚 3 𝑘𝑚 = 6 𝑐𝑚 𝑥 𝑘𝑚 5x = 18 5𝑥 5 = 18 5 x = 3.6 km from Knivsta to Stockholm

The height of the symbol in the accompanying drawing is 1. 5 inches The height of the symbol in the accompanying drawing is 1.5 inches. The actual symbol will be 12 inches tall once it is placed on a sign. If the width of this symbol is 1 inch, how wide will the actual symbol be? First find the scale factor by putting model over actual: 1.5 𝑖𝑛 12𝑖𝑛 1.5 𝑖𝑛 12 𝑖𝑛 = 1 𝑖𝑛 𝑥 𝑖𝑛 1.5x = 12 1.5𝑥 1.5 = 12 1.5 X = 8 in wide

What is the scale factor from the small rectangle to the large? 2 in 6 in 1 in x in First find the scale factor by putting model over actual: 2 𝑖𝑛 6 𝑖𝑛 2 𝑖𝑛 6 𝑖𝑛 = 1 𝑖𝑛 𝑥 𝑖𝑛 2x = 6 2𝑥 2 = 6 2 X = 3 in wide

An outline of Florida is sketched on a grid An outline of Florida is sketched on a grid. If each grid unit represents 150 miles. What is the best estimate of the length of Florida’s coastline? First find the scale factor by putting model over actual: 1.5 𝑖𝑛 12𝑖𝑛 1 𝑢𝑛𝑖𝑡 150 𝑚𝑖𝑙𝑒𝑠 = 4.5 𝑥 𝑚𝑖𝑙𝑒𝑠 1x = 675 1𝑥 1 = 675 1 X = 675 miles

The Sears Tower is 1450 feet. Jeff wanted to make a scale for his class project, but his mother’s car can hold only 36 inches tall model. Which of the following scales is closest to the scale Jeff needs? First find the scale factor by putting model over actual: 36 𝑖𝑛 1450 𝑓𝑡 36 𝑖𝑛 1450 𝑓𝑡 = 1 𝑖𝑛 𝑥 𝑓𝑡 36x = 1450 36𝑥 36 = 1450 36 X = 40 ft correct answer B

A photograph measures 4 inches wide and 5 inches long A photograph measures 4 inches wide and 5 inches long. If you have the photograph enlarged to fit a frame 36 inches long, what is the widest the photograph can be? First find the scale factor by putting model over actual: 5 𝑖𝑛 36 𝑖𝑛 5 𝑖𝑛 36 𝑖𝑛 = 4 𝑖𝑛 𝑥 𝑖𝑛 5x = 144 5𝑥 5 = 144 5 X = 28.8 in wide

Aaron bought a model airplane Aaron bought a model airplane. The model used a scale of 1 4 inch = 50 feet. If Aaron’s model airplane is 18 inches long, how long is a real airplane? First find the scale factor by putting model over actual: .25 𝑖𝑛 50 𝑓𝑡 .25 𝑖𝑛 50 𝑓𝑡 = 18 𝑖𝑛 𝑥 𝑓𝑡 .25x = 900 .25𝑥 .25 = 900 .25 X = 3600 ft

If the rectangle below is enlarged using a scale factor of 1cm: 2 If the rectangle below is enlarged using a scale factor of 1cm: 2.5cm, what will be the perimeter and area of the new rectangle? First find the scale factor by putting model over actual: 1 𝑐𝑚 2.5 𝑐𝑚 1 𝑐𝑚 2.5 𝑐𝑚 = 9 𝑐𝑚 𝑥 𝑐𝑚 1x = 22.5 1𝑐𝑚 2.5 𝑐𝑚 = 5 𝑐𝑚 𝑥 𝑐𝑚 1𝑥= 12.5 Perimeter add up all sides: 22.5 +22.5+12.5+12.5 = 70 cm