What is the area of rectangular region R ?

[sanjib]

What is the area of rectangular region R ?
(1) Each diagonal of R has length 5.
(2) The perimeter of R is 14.
IMO E
because only 30.60.90 angle situation comply to say that it would be 3:4:5 the both side and Hypt.
However it only angle we know is 90 then it could be any angle and not has to be 30 and 60

[Bryant@VeritasPrep]

this seems to me that both together are sufficient since you end up with two equations, two unknowns, namely:

2a+2b = 14
and
a^2 + b^2 = 25

which is solvable

[engg.manik]

The correct answer acc to me is C.

as from St 1 a^2 + b^2 = 25

from st 2 - 2a + 2b = 14 ---> (a+b)^2=7^2
solving will get 25 + 2ab = 49
ab = 12 which is the area.

I hope it helps

[maihuna]

What is the area of rectangular region R ?
(1) Each diagonal of R has length 5.
(2) The perimeter of R is 14.
IMO E
because only 30.60.90 angle situation comply to say that it would be 3:4:5 the both side and Hypt.
However it only angle we know is 90 then it could be any angle and not has to be 30 and 60

diagonal : (a^2+b^2)^1/2 = 5 => a^2+b^2 = 25
Perimeter: 2(a+b) = 14 => a+b = 7

=> a^2+b^2 = (a+b)^2-2ab => 2ab = -a^2+b^2 + (a+b)^2
=> 2ab = -25+49 = 24 => ab = 12 = area C