SME
Grade 7 Math · Problem type
Scaled copies on a grid
Use this for “A 4 by 3 picture is enlarged to 12 wide. How tall is it?”
Diagram
Scale factor 3: every length times 3
Width: 4 × 3 = 12
Height: 3 × 3 = 9
This is an example. Type your own values to start a new problem.
W
=
k
×
w
H
=
k
×
h
Formulas
W
=
k
×
w
(copy
width
=
scale
factor
×
width)
12 = 3 × 4
H
=
k
×
h
(copy
height
=
scale
factor
×
height)
9 = 3 × 3
Assumptions
•
A scaled copy multiplies every length by the same scale factor.
•
Its angles stay the same, so the copy has the same shape.
•
A factor under 1 makes a smaller copy.
Step-by-step
WE KNOW
k = 3 (scale factor), w = 4 (width), h = 3 (height)
FIND
copy width (W), copy height (H)
Step 1 · Find copy width (W)
Use W = k × w (copy width = scale factor × width)
Multiply the length by the scale factor.
W
=
3
×
4
W
=
12
Step 2 · Find copy height (H)
Use H = k × h (copy height = scale factor × height)
Multiply the length by the scale factor.
H
=
3
×
3
H
=
9
Check
Put the numbers back in. Both sides should match.
12 = 3 × 4 ✓
9 = 3 × 3 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
Related lessons
Scale drawings
Main lesson
Map distances in miles
Use this for “On a map, 1 inch represents 25 miles. Two towns are 3.5 inches apart. How far apart are they?”
Map distances in kilometers
Use this for “On a map, 1 cm represents 5 km. How far is a 7.2 cm route?”
Scale factor and area
Use this for “A triangle with base 4 and height 3 is copied at scale factor 2. What is the copy’s area?”
Scaled copy or not?
Use this for “Which figure is a scaled copy of the original?”
The same scale, said another way
Use this for “Which scale is the same as 1 cm to 50 m?”