If the ratio of three sides of a triangle is -3- -4- -5- then it is a right angle triangle-

The correct option is B False Let the side be √(3)x,√(4)x,√(5)x Squaring (√(3)x)^2=3x^2,(√(4)x)^2=4x^2,(√(5)x)^2=5x^2 so here 3x^2+4x^2≠ 5x^2, hence it is not ...

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Standard X

Mathematics

Basic Proportionality Theorem

If the ratio ...

Question

If the ratio of three sides of a triangle is $\sqrt{3} : \sqrt{4} : \sqrt{5},$ then it is a right angle triangle.

True

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False

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Solution

The correct option is B
False

Let the side be $\sqrt{3} x, \sqrt{4} x, \sqrt{5} x$

Squaring $(\sqrt{3} x)^{2} = 3 x^{2}, (\sqrt{4} x)^{2} = 4 x^{2}, (\sqrt{5} x)^{2} = 5 x^{2}$

so here $3 x^{2} + 4 x^{2} \neq 5 x^{2},$ hence it is not right-angle triangle

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If the ratio of three sides of a triangle is √3:√4:√5, then it is a right angle triangle.

The correct option is B False Let the side be √3x,√4x,√5x Squaring (√3x)2=3x2,(√4x)2=4x2,(√5x)2=5x2 so here 3x2+4x2≠5x2, hence it is not right-angle triangle

If the ratio of three sides of a triangle is $\sqrt{3} : \sqrt{4} : \sqrt{5},$ then it is a right angle triangle.

The correct option is B
False

Let the side be $\sqrt{3} x, \sqrt{4} x, \sqrt{5} x$

Squaring $(\sqrt{3} x)^{2} = 3 x^{2}, (\sqrt{4} x)^{2} = 4 x^{2}, (\sqrt{5} x)^{2} = 5 x^{2}$

so here $3 x^{2} + 4 x^{2} \neq 5 x^{2},$ hence it is not right-angle triangle