Find the ratio of the sides of a square to an equilateral triangle if they have equal perimeter.
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it may be 4 is to 3.....
mariya9:
roght but how. plz explain
Considering their equal perimeter, a side of an equilateral triangle t equals to 43 of a side of a square s because
Perimeter=3⋅t=4⋅s
Therefore,
t=43s
The altitude of an equilateral triangle with a side t equals to t√32.
The area of an equilateral triangle with a side t is
SΔ=12⋅t⋅t√32=t2√34
The area of a square with a side s is
S□=s2
Their ratio is:
SΔS□=t2√34s2
Substituting t=43s, we get
SΔS□=16s2√39⋅4s2=4√39
Perimeter=3⋅t=4⋅s
Therefore,
t=43s
The altitude of an equilateral triangle with a side t equals to t√32.
The area of an equilateral triangle with a side t is
SΔ=12⋅t⋅t√32=t2√34
The area of a square with a side s is
S□=s2
Their ratio is:
SΔS□=t2√34s2
Substituting t=43s, we get
SΔS□=16s2√39⋅4s2=4√39
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