

4. Mia’s hometown has a rectangular park while JM’s hometown has a square park with a side length of 48 m. In their conversation:
JM: How big is your park?
Mia: If you go around your park thrice, then it’s like you go around our park twice.
If the width of the park in Mia’s hometown is 70 m, what is its length (in m)?
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To find the length of the rectangular park in Mia's hometown, we need to use the information from the dialogue between JM and Mia.
Area of JM's square park:
Side = 48 m
Perimeter = 4 * 48 = 192 m
According to Mia, if you go around JM's park three times, it is equal to going around Mia's park twice. Therefore:
The perimeter of Mia's park (rectangle) must be:
Mia's perimeter
=
3
2
×
192
=
288
m
Mia's perimeter=
2
3
×192=288 m
The formula for the perimeter of a rectangle is:
P
=
2
×
(
d
+
r
)
P=2×(d+r)
Where
d
d is the length and
r
r is the width. We already know the width
r
=
70
r=70 m:
288
=
2
×
(
d
+
70
)
288=2×(d+70)
Divide both sides by 2:
144
=
d
+
70
144=d+70
Solve the equation:
d
=
144
−
70
=
74
m
d=144−70=74 m
So the length of the park in Mia's hometown is 74 m.
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