Each sides of an equilateral triangle is 10 cm . If its perimeter is equal to the perimeter of a square , find the side of the sq square.
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The Median AM divides the side BC in two equal parts . BM = MC
Lets call this x.
As BC = BM + MC = x + x = 2x.
As △ABC being a equilateral triangle AB = BC = 2x.
Now see this triangle

In △ABM,
AB2=BM2+AM2AB2=BM2+AM2
(2x)2=x2+102(2x)2=x2+102
4x2−x2=1004x2−x2=100
3x2=1003x2=100
x=103√x=103
AB = 2x = 2×103√=203√2×103=203
Thus the perimeter of equilateral triangle ABC is 3 × AB = 203√×3203×3
=203–√=203cm.
Lets call this x.
As BC = BM + MC = x + x = 2x.
As △ABC being a equilateral triangle AB = BC = 2x.
Now see this triangle

In △ABM,
AB2=BM2+AM2AB2=BM2+AM2
(2x)2=x2+102(2x)2=x2+102
4x2−x2=1004x2−x2=100
3x2=1003x2=100
x=103√x=103
AB = 2x = 2×103√=203√2×103=203
Thus the perimeter of equilateral triangle ABC is 3 × AB = 203√×3203×3
=203–√=203cm.
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Answer:
perimeter of a equilateral triangle =3×(length of a side)
thus, perimeter of a triangle =3 (10 )=30cm.
perimeter of a square =4×side
30 cm= 4×side
side = 30/4
side =7.5cm.
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