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Meghna Thapar 4 years, 4 months ago
Angles opposite to equal sides of a triangle are equal. Sides opposite to equal angles of a triangle are equal. Each angle of an equilateral triangle is of 60°. If three sides of one triangle are equal to three sides of the other triangle, then the two triangles are congruent (SSS Congruence Rule). An isosceles triangle therefore has both two equal sides and two equal angles. The name derives from the Greek iso (same) and skelos (leg). A triangle with all sides equal is called an equilateral triangle, and a triangle with no sides equal is called a scalene triangle.
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Yogita Ingle 4 years, 4 months ago
(a²-b²)³+(b²-c²)³+(c²-a²)³
We know that if x + y + z =0 then x3 + y3 + z3 = 3xyz
Here x = a²-b², y = b²-c² and z = c²-a²
a²-b² + b²-c² + c²-a² = 0
Hence (a²-b²)³+(b²-c²)³+(c²-a²)³ = 3(a²-b²)(b²-c²)(c²-a²)³
= 3(a + b)(a − b)(b + c)(b − c)(c + a)(c − a)
= 3(a + b)(b + c)(c + a)(a − b)(b − c)(c − a)
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Yogita Ingle 4 years, 4 months ago
a = 3 cm, b = 4 cm and c = 5 cm
Area of perimeter = 3+ 4+ 5 =12 cm
semi-perimeter = 12/2 = 6 cm
Area of triangle = √ s (s-a)(s-b)(s-c)
= √ 6(6 - 3) (6-4)(6-6)
= √6 (3)(2)(1)
= √36
= 6 sq. cm.
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Yogita Ingle 4 years, 4 months ago
Since, a3 + b3 + c3 − 3abc = (a + b + c)(a2 + b2 + c2 − bc − ca −ab)
Given, a + b + c = 0
∴ a3 + b3 + c3− 3abc = 0
∴ a3 + b3 + c3 = 3abc
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Piyush Mandhare 4 years, 4 months ago
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