The three sides of a triangle is 3x-2- 3x-2 and -24x -Prove that they form a right-angled triangle- -2 Marks-

Let the triangle be ABC, where AB=3x+2 ⇒ AB^2=(3x+2)^2=9x^2+12x+4 nbsp;[0.5 Mark] nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; ...

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Standard VIII

Mathematics

Converse of Pythagoras Theorem

The three sid...

Question

The three sides of a triangle is $3 x + 2, 3 x - 2$ and $\sqrt{24 x} .$ Prove that they form a right-angled triangle. [2 Marks]

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Solution

$Let the triangle be △ A B C, where A B = 3 x + 2 \Rightarrow A B^{2} = (3 x + 2)^{2} = 9 x^{2} + 12 x + 4 [0.5 M a r k] A C = 3 x - 2 \Rightarrow A C^{2} = (3 x - 2)^{2} = 9 x^{2} - 12 x + 4 [0.5 M a r k] B C = \sqrt{24 x} \Rightarrow B C^{2} = 24 x [0.5 M a r k] A C^{2} + B C^{2} = 9 x^{2} - 12 x + 4 + 24 x A C^{2} + B C^{2} = 9 x^{2} + 12 x + 4 = A B^{2}$

By the converse of Pythagoras' theorem, the given sides form a right-angled triangle. [0.5 Mark]

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The three sides of a triangle is 3x+2,3x−2 and √24x.Prove that they form a right-angled triangle. [2 Marks]

Let the triangle be△ABC,whereAB=3x+2⇒AB2=(3x+2)2=9x2+12x+4 [0.5Mark]AC=3x−2⇒AC2=(3x−2)2=9x2−12x+4 [0.5Mark]BC=√24x⇒BC2=24x [0.5Mark]AC2+BC2=9x2−12x+4+24x AC2+BC2=9x2+12x+4=AB2 By the converse of Pythagoras' theorem, the given sides form a right-angled triangle. [0.5 Mark]

The three sides of a triangle is $3 x + 2, 3 x - 2$ and $\sqrt{24 x} .$ Prove that they form a right-angled triangle. [2 Marks]