Page 123 - Math Course 3 (Book 2)

Similarity of Polygons

Scales on Maps
The two polygons are similar. Find the scale factor
of polygon ABCDE to polygon RSTUV.
Example
The scale factor is the ratio of the lengths of any
two corresponding sides.
1
The scale on the map of a city is inch equals 2
4
miles. On the map, the width of the city at its
AB = 6 or 3 3
RS 4 2 widest point is 3 inches. The city hosts a bicycle
4
race across town at its widest point. Tashawna
bikes at 10 miles per hour. How long will it take her
3 to complete the race?

Answer
2 Explore
1
Every or 0.25 inch equals 2 miles. The distance
4
3
across the city at its widest point is 3 or 3.75 in.
4
Plan
Enlargement or Reduction of a Figure Create a proportion relating the measurements to
the scale to find the distance in miles. Then use the
Example formula d=rt to find the time.

Solve
Rectangle WXYZ is similar to rectangle PQRS with
a scale factor of 1.5. If the length and width of inches → 0.25 = 3.75 ← inches
PQRS are 10 meters and 4 meters, respectively, inches → 2 x ← miles
what are the length and width of rectangle WXYZ?
0.25x = 75 Cross products.
x = 30 Divide each side by 0.25.
Write proportions for finding side measures. Let The distance across the city is 30 miles.
one long side of each WXYZ and PQRS be WX and d = rt
PQ and one short side of each WXYZ and PQRS be
XY and QR. 30 = 10t d = 30 and r = 10
3 = t Divide each side by 10.

WXYZ → WX = 3 WXYZ → XY = 3 It would take Tashawna 3 hours to bike across town.
PQRS → PQ 2 PQRS → QR 2 Examine
To determine whether the answer is reasonable,
ℓ 3 w 3 reexamine the scale. If 0.25 inches = 2 miles, then
10 = 2 4 = 2 4 inches = 32 miles. The distance across the city
is approximately 32 miles. At 10 miles per hour,
2ℓ = 30 2w = 12 the ride would take about 3 hours. The answer is
ℓ = 15 w = 6 reasonable.

Answer ℓ = 15m, w = 6m Answer 3 hours

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