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What is the length of the hypotenuse of ΔABC ?

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What is the length of the hypotenuse of ΔABC ?  [#permalink]

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21 Sep 2019, 18:08
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Difficulty:

65% (hard)

Question Stats:

52% (02:01) correct 48% (01:58) wrong based on 66 sessions

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What is the length of the hypotenuse of ΔABC ?

(1) The lengths of the three sides of ΔABC are consecutive even integers.
(2) The hypotenuse of ΔABC is 4 units longer than the shorter leg.

DS18041.01
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What is the length of the hypotenuse of ΔABC ?  [#permalink]

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Updated on: 28 Sep 2019, 11:09
What is the length of the hypotenuse of ΔABC?

STATEMENT (1) The lengths of the three sides of ΔABC are consecutive even integers.
let the two legs be --2n and 2n+2 hypotenuse 2n+4
then 4$$(n+2)^2$$ = 4$$n^2$$+4$$(n+1)^2$$
(n+1)(n-3)=0
n =3 (n cant be -ve value)
hypotenuse = 10
SUFFICIENT

STATEMENT (2) The hypotenuse of ΔABC is 4 units longer than the shorter leg.
let the shorter leg = x
hypotenuse = x+4
since we don't know the value of x we can't find the value of the hypotenuse
INSUFFICIENT

Originally posted by shridhar786 on 22 Sep 2019, 11:22.
Last edited by shridhar786 on 28 Sep 2019, 11:09, edited 1 time in total.
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Re: What is the length of the hypotenuse of ΔABC ?  [#permalink]

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22 Sep 2019, 16:18
It is just extended version of your explanation for statement 1.
Statement 1 is about 3 consecutive even integers which are sides of right angle triangle.
So 6, 8 and 10 is right triplet satisfying this condition.

shridhar786 wrote:
What is the length of the hypotenuse of ΔABC?

STATEMENT (1) The lengths of the three sides of ΔABC are consecutive even integers.
let the two legs be --n and n+1 hypotenuse n+2
then $$(n+2)^2$$ = $$n^2$$+$$(n+1)^2$$
(n+1)(n-3)=0
n =3 (n cant be -ve value)
hypotenuse = 5
SUFFICIENT

STATEMENT (2) The hypotenuse of ΔABC is 4 units longer than the shorter leg.
let the shorter leg = x
hypotenuse = x+4
since we don't know the value of x we can't find the value of the hypotenuse
INSUFFICIENT

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Re: What is the length of the hypotenuse of ΔABC ?  [#permalink]

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26 Sep 2019, 21:25
gmatt1476 wrote:
What is the length of the hypotenuse of ΔABC ?

(1) The lengths of the three sides of ΔABC are consecutive even integers.
(2) The hypotenuse of ΔABC is 4 units longer than the shorter leg.

DS18041.01

Is a hypotenuse present only in right triangles?
the measures could be 10-12-14
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Re: What is the length of the hypotenuse of ΔABC ?  [#permalink]

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26 Sep 2019, 21:48
Hypotenuse is defined only for the right angled triangle.

Hypotenuse is the longest side of the right angled triangle.

nurba92 wrote:
gmatt1476 wrote:
What is the length of the hypotenuse of ΔABC ?

(1) The lengths of the three sides of ΔABC are consecutive even integers.
(2) The hypotenuse of ΔABC is 4 units longer than the shorter leg.

DS18041.01

Is a hypotenuse present only in right triangles?
the measures could be 10-12-14

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Re: What is the length of the hypotenuse of ΔABC ?  [#permalink]

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02 Oct 2019, 16:50
Conditions of statement 1 mandate that the triangle be a 6-8-10 triangle...

Try variations of this and you will see that the gap in side lengths increases
6-8-10
12-16-20
24-32-40 ... and so on

The alternative is to solve statement 1 more algebraically
Side 1 length = n
Side 2 length = (n+2)
Hypotenuse = (n+4)

Solve via pythag theorem and you will see that n= 6

Statement 2
There are no constraints on this statement. If you solve algebraically as in statement 1 above you will see that the value of the hypotenuse increases if we take a higher base for the shortest leg.
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Re: What is the length of the hypotenuse of ΔABC ?   [#permalink] 02 Oct 2019, 16:50
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