ABCD forms a rectangle with sides x and y. z is the

Question

ABCD forms a rectangle with sides x and y. z is the diagonal. What is the perimeter of ABCD?

1. x-y = 7
2. z = 13

x^2 + y^2 = z^2
x^2 + y^2 = 169

(x-y)^2 = 7^2
x^2 - 2xy + y^2 = 49
x^2 + y^2 - 2xy = 49
169 - 2xy = 49
120 = 2xy
xy=60

Can someone show me what the next step is?

OA is C

srp · Answer

12*5 = 60

squaring may not be required here

sarveshgupta11 · Answer

x^2 + y^2 = 13^2
(x+y) (x-y) = 169
x+y = 169/7
2(x+y) = 2*169/7

ANS C

GMATBLACKBELT · Answer

this isn't an appropriate method.

(x+y)(x-y) --> x^2-y^2

Skewed · Answer

x-y = 7; x = 7+y
z = 13

x^2 + y^2 = z^2
(7+y)^2 + y^2 = 169
49 + 14y + 2y^2 = 169
y^2 + 7y - 60 = 0

(y-5)(y+12) =0
y=-12 or y = 5

y = 5 and x = 12; P = 34

StartupAddict · Answer

Picture it in your head.

1 tells you X is 7 longer than Y. But that could be 1 / 8, 2 / 9, which would give you different parameters.

2 just tells you the diagonal, but again the two sides could be in a bunch of combinations.

put them together and you have enough info.

I just visualize rectangles and I make them bigger and smaller..........

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