SME
Grade 10 Math · Problem type
Scale factor, perimeter and area
Use this for “A 3 by 4 rectangle is enlarged by 2.5. What are the new perimeter and area?”
Diagram
Scale factor 2.5: every length times 2.5
Width: 3 × 2.5 = 7.5
Height: 4 × 2.5 = 10
Area: 12 × 2.5 × 2.5 = 75
This is an example. Type your own values to start a new problem.
A₂
=
k
2
×
A
w
Width
example
h
Height
example
W
Copy width
calculated
H
Copy height
calculated
P
Perimeter
worked out (not typed)
P₂
Copy perimeter
calculated
Formulas
W
=
k
×
w
7.5 = 2.5 × 3
H
=
k
×
h
10 = 2.5 × 4
P
=
2
×
(
w
+
h
)
14 = 2 × (3 + 4)
A
=
w
×
h
12 = 3 × 4
P₂
=
k
×
P
35 = 2.5 × 14
A₂
=
k
2
×
A
75
=
2.5
2
×
12
Assumptions
•
Lengths are counted in grid squares, areas in square units.
•
Every length of the copy is k times the original, a perimeter or circumference too.
•
Every area is k² times the original: k in both directions.
Step-by-step
WE KNOW
w = 3, h = 4, k = 2.5
FIND
copy width (W), copy height (H), perimeter (P), area (A), copy perimeter (P₂), copy area (A₂)
Step 1 · Find copy width (W)
Use W = k × w
Multiply the width by the scale factor.
W
=
2.5
×
3
W
=
7.5
Step 2 · Find copy height (H)
Use H = k × h
Multiply the height by the scale factor.
H
=
2.5
×
4
H
=
10
Step 3 · Find perimeter (P)
Use P = 2 × (w + h)
The perimeter is twice the sum of the width and the height.
P
=
2
×
(3
+
4)
P
=
2
×
7
P
=
14
Step 4 · Find area (A)
Use A = w × h
The area of a rectangle is width times height.
A
=
3
×
4
A
=
12
Step 5 · Find copy perimeter (P₂)
Use P₂ = k × P
Multiply the perimeter by the scale factor.
P₂
=
2.5
×
14
P₂
=
35
Step 6 · Find copy area (A₂)
Use A₂ = k² × A
Every
area
is
multiplied
by
k
2
.
A₂
=
2.5
2
×
12
A₂
=
6.25
×
12
A₂
=
75
Check
Put the numbers back in. Both sides should match.
7.5 = 2.5 × 3 ✓
10 = 2.5 × 4 ✓
14 = 2 × (3 + 4) ✓
12 = 3 × 4 ✓
35 = 2.5 × 14 ✓
75
=
2.5
2
×
12
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
Translations, rotations, reflections and dilations
Proportional relationships and the constant of proportionality
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