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What is the value of z? (1) The lengths of the sides of a triangle AB

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Bunuel
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What is the value of z? (1) The lengths of the sides of a triangle AB [#permalink] New post   15 Dec 2020, 01:15
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What is the value of z?

(1) The lengths of the sides of a triangle ABC are 3, 4 and z.
(2) ABC is a right angled triangle.


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E
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TarunKumar1234
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Re: What is the value of z? (1) The lengths of the sides of a triangle AB [#permalink] New post   15 Dec 2020, 02:10
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Stat1: If one side is 4 and another is 3 then, 3rd side in triangle can have multiple size possibilities. So, It is NOT sufficient to get Z value.

Stat2: Knowing triangle is right angle triangle is NOT sufficient to get one side.

Combining 1 and 2: Do we know, which angle is 90 degree and which sides are 3 and 4. So, We can multiple value of Z. It is not sufficient as well.

So, I think. E :)
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Re: What is the value of z? (1) The lengths of the sides of a triangle AB [#permalink] New post   15 Dec 2020, 04:00
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Hmm, there had to be a trap and there it is!

(A) - Two side are given ,i.e. 3 and 4. The third side can be anything. 5,6,7,8...(as long as they satisfy the rule of third side>sum of two other sides)
Not sufficient.

(B)- We are not aware about the length of the other sides.
Not sufficient.

Combining, we STILL do not know where the triangle is right angled :D
That was the trap. We could have very well imagined the beautiful 3,4,5 if the angle was specified.

IMO E.
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Re: What is the value of z? (1) The lengths of the sides of a triangle AB [#permalink] New post   15 Dec 2020, 05:38
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Quote:
What is the value of z?

(1) The lengths of the sides of a triangle ABC are 3, 4 and z.
(2) ABC is a right angled triangle.


1) The lengths of the sides of a triangle ABC are 3, 4 and z.

We know for any triangle with sides a, b, and c
c>a-b
c<a+b
Here, x =4, y = 3
So, z>4-3 > 1
and z<4+3 < 7
Z could be 2,3,4,5 etc.
Insufficient

2) ABC is a right angled triangle.
Clearly Insufficient

1+2 Combined,
x=4, y=3, z=?
If x is the base and y is the perpendicular, then \(z^2\) = \(3^2\) + \(4^2\) => z = 5
If x is the hypotenuse and y is the base, then perpendicular \(z^2\) = \(4^2\) - \(3^2\) => z = \(\sqrt{16-9}\) =\(\sqrt{7}\)

Still 2 values of Z. Insufficient

(E)
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Re: What is the value of z? (1) The lengths of the sides of a triangle AB [#permalink] New post   15 Dec 2020, 10:23
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What is the value of z?

(1) The lengths of the sides of a triangle ABC are 3, 4 and z.
(2) ABC is a right angled triangle.



1) Asking about Z and then z is not given.. A) & D) out | Z could be anything under 4-3 <z < 3+4
2) ABC is right angled and nothing given B) out

Combining 1 & 2
z = \sqrt{3^2 + 4^2} = \sqrt{25} = 5
or

z^2 + 3^2 = 4^2 => z^2 = 16-9 => z = \sqrt{7} ~ 2.something

Even after combining getting two options.
IMO (E)
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Re: What is the value of z? (1) The lengths of the sides of a triangle AB [#permalink] New post   15 Dec 2020, 14:18
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What is the value of z?

(1) The lengths of the sides of a triangle ABC are 3, 4 and z.
Z can hold multiple values. Z can be 5 or 6. Insufficient.

(2) ABC is a right angled triangle.
We do not have any information about the sides - Insufficient

(1) + (2) together
ABC is a right angled triangle, but we sill did not know the specific sides and s Z can hold multiple values.

both options together are Insufficient

Ans E
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Re: What is the value of z? (1) The lengths of the sides of a triangle AB [#permalink]
15 Dec 2020, 14:18
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Bunuel
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