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

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
If a right triangle has a longest side of 10, which of the following  [#permalink]

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07 Sep 2018, 00:04
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Difficulty:

25% (medium)

Question Stats:

72% (00:56) correct 28% (01:24) wrong based on 31 sessions

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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]

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07 Sep 2018, 07:17
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]

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09 Sep 2018, 00:57
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.

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If a right triangle has a longest side of 10, which of the following   [#permalink] 09 Sep 2018, 00:57
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