the area of circle inscribed in an equilateral triangle is 154 cm2 . find the perimeter of the triangle.
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then we know, πr²=154cm². then 22/7×r²=154=>r=7cm.
and let the side of the triangle=a cm. then we know that all the angles of an equilateral triangle=60°. so from the center of the circle let a ∆ABC be formed in which BC is the radius and <BAC=30°( half of the angle). then since BC=7cm.so
tan30°=1/√3=7/AC=>AC=7√3cm.and hence one side of the equilateral triangle=2×7√3=14√3cm and
thus perimeter of the triangle=3×14√3=42√3cm.
and let the side of the triangle=a cm. then we know that all the angles of an equilateral triangle=60°. so from the center of the circle let a ∆ABC be formed in which BC is the radius and <BAC=30°( half of the angle). then since BC=7cm.so
tan30°=1/√3=7/AC=>AC=7√3cm.and hence one side of the equilateral triangle=2×7√3=14√3cm and
thus perimeter of the triangle=3×14√3=42√3cm.
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