SME
Grade 7 Math · Geometry
Scale drawings
Use this for “The scale is 1 inch to 6 feet. A wall is 3.5 inches on the drawing. What is its actual length?”
Diagram
d = 3.5 in on the top line sits over 21 ft on the bottom line: each 1 above is 6 below.
k = 72 (scale factor: real inches for 1 inch drawn)
This is an example. Type your own values to start a new problem.
a (ft)
=
s
×
d (in)
k
Scale factor: real inches for 1 inch drawn
worked out (not typed)
Formulas
a
=
s
×
d
(actual
length
=
feet
for
1
inch
on
the
drawing
×
length
on
the
drawing)
21 = 6 × 3.5
k
=
12
×
s
(scale
factor:
real
inches
for
1
inch
drawn
=
12
×
feet
for
1
inch
on
the
drawing)
72 = 12 × 6
Assumptions
•
A scale says what 1 unit on the drawing stands for: 1 in represents 6 ft.
•
Every length on the drawing is multiplied by the same scale.
•
The scale factor has no units: both lengths in inches, then actual ÷ drawing.
•
Angles do not change.
Step-by-step
WE KNOW
s = 6 (feet for 1 inch on the drawing), d = 3.5 in (length on the drawing)
FIND
actual length (a), scale factor: real inches for 1 inch drawn (k)
Step 1 · Find actual length (a)
Use a = s × d (actual length = feet for 1 inch on the drawing × length on the drawing)
Each
inch
on
the
drawing
stands
for
s
feet.
a
=
6
×
3.5
a
=
21
ft
Step 2 · Find scale factor: real inches for 1 inch drawn (k)
Use k = 12 × s (scale factor: real inches for 1 inch drawn = 12 × feet for 1 inch on the drawing)
Put
both
lengths
in
inches:
s
feet
is
12
×
s
inches
for
every
inch
drawn.
k
=
12
×
6
k
=
72
Check
Put the numbers back in. Both sides should match.
21 = 6 × 3.5 ✓
72 = 12 × 6 ✓
Topic check
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