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If a right triangle has a longest side of 10, which of the following

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Bunuel
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If a right triangle has a longest side of 10, which of the following [#permalink] New post   07 Sep 2018, 01:04
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If a right triangle has a longest side of 10, which of the following is not a possible value for the other two sides?


A. 5 and \(5\sqrt{3}\)

B. \(5\sqrt{2}\) and \(2\sqrt{5}\)

C. 6 and 8

D. 7 and \(\sqrt{51}\)

E. \(7\sqrt{2}\) and \(\sqrt{2}\)
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If a right triangle has a longest side of 10, which of the following [#permalink] New post   07 Sep 2018, 08:17
Bunuel wrote:
If a right triangle has a longest side of 10, which of the following is not a possible value for the other two sides?


A. 5 and \(5\sqrt{3}\)

B. \(5\sqrt{2}\) and \(2\sqrt{5}\)

C. 6 and 8

D. 7 and \(\sqrt{51}\)

E. \(7\sqrt{2}\) and \(\sqrt{2}\)


Note:-
1) Hypotenuse is the longest side in a right angled triangle.
2) Square of hypotenuse=sum of the squares of other two sides (As per Pythagoras theorem)

So, Sum of the square of other two sides must be 100.

A. \(5^2+(5\sqrt{3})^2=100\). DISCARD
B. \((5\sqrt{2})^2\)+\((2\sqrt{5})^2\neq{100}\). KEEP

Ans. (B)
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If a right triangle has a longest side of 10, which of the following [#permalink] New post   09 Sep 2018, 01:57
In a right angled triangle, sum of squares of the two sides is equal to square of the hypotenuse.

A. 5 and \(5\sqrt{3}\)
\(5^2+(5\sqrt{3})^2\) = 25+75=100

B. \(5\sqrt{2}\) and \(2\sqrt{5}\)
\((5\sqrt{2})^2+(2\sqrt{5})^2\) = 50+20=70 ≠ 100. CORRECT.

C. 6 and 8
36+64=100

D. 7 and \(\sqrt{51}\)
49+51=100

E. \(7\sqrt{2}\) and \(\sqrt{2}\)
98+2=100.

Answer B.
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Re: If a right triangle has a longest side of 10, which of the following [#permalink] New post   29 Nov 2022, 08:35
Bunuel wrote:
If a right triangle has a longest side of 10, which of the following is not a possible value for the other two sides?


A. 5 and \(5\sqrt{3}\)

B. \(5\sqrt{2}\) and \(2\sqrt{5}\)

C. 6 and 8

D. 7 and \(\sqrt{51}\)

E. \(7\sqrt{2}\) and \(\sqrt{2}\)

\((5\sqrt{2}\) and \(2\sqrt{5})^2 = 50 + 20 => 70\), hence Answer will be (B)
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Re: If a right triangle has a longest side of 10, which of the following [#permalink]
29 Nov 2022, 08:35
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