The three side of triangle is 3 x-2-3 x-2- -24 x- They are forming a right-angled triangle-

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Standard X

Mathematics

Distance Formula

The three sid...

Question

The three side of triangle is (3x+2), (3x-2), $\sqrt{24} x$ . They are forming a right-angled triangle.

True

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False

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Solution

The correct option is A
True

$Let triangle be ABC A B = (3 x + 2) A B^{2} = (3 x + 2)^{2} = 9 x^{2} + 12 x + 4 A C = (3 x - 2) A C^{2} = (3 x - 2)^{2} = 9 x^{2} - 12 x + 4 B C = \sqrt{24} x B C^{2} = 24 x We can A C^{2} + B C^{2} = 9 x^{2} - 12 x + 4 + 24 x A C^{2} + B C^{2} = 9 x^{2} + 12 x + 4 A C^{2} + B C^{2} = A B^{2} Hence they form a right-angled triangle$

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The three side of triangle is (3x+2), (3x-2), √24x. They are forming a right-angled triangle.

The correct option is A True Let triangle be ABCAB=(3x+2)AB2=(3x+2)2=9x2+12x+4AC=(3x−2)AC2=(3x−2)2=9x2−12x+4BC=√24xBC2=24xWe can AC2+BC2=9x2−12x+4+24x AC2+BC2=9x2+12x+4 AC2+BC2=AB2Hence they form a right-angled triangle

The three side of triangle is (3x+2), (3x-2), $\sqrt{24} x$ . They are forming a right-angled triangle.