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
A
...
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
A
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