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The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown.What is the smallest possible perimeter of the triangle, rounded to the nearest
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Apr 8, 2018
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The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown.What is the smallest possible perimeter of the triangle, rounded to the nearest hundredth?
Mathematics
high-school
Alaeddin AL Zeybek
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Alaeddin AL Zeybek
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Let "x" be the longest side and "y" be each of
remaining sides
If the triangle is аcute
then:
y² + y² > x²
2y
² > 30²
2y² > 900
y² > 450
y >
√450
y > 21.21 ←
to the nearest hundredth
This means the length of each of the remaining sides is not less than 21.22 in (to the nearest hundredth), so
the smallest possible perimeter of the triangle =
30 + 21.22 + 21.22 =
72.44 in.
Jfs
answered
Apr 14, 2018
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Jfs
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