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bmwhype2
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Is the perimeter of a rectangle bigger than 8 inches? 1. the 17 Oct 2007, 11:00
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Is the perimeter of a rectangle bigger than 8 inches?

1. the diagonal of the rectangle is twice as long as its shorter side
2. The diagonal is 4 inches longer than its shorter side



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Is the perimeter of a rectangle bigger than 8 inches? 1. the Updated on: 17 Oct 2007, 12:01
Originally posted by IrinaOK on 17 Oct 2007, 11:36.
Last edited by IrinaOK on 17 Oct 2007, 12:01, edited 1 time in total.
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EDITTED***

Should be B,

see explanation below by hyperstorm.
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Is the perimeter of a rectangle bigger than 8 inches? 1. the 17 Oct 2007, 11:53
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I think C would do.

Let's consider half of the rectangle, i.e., a triangle.

Diagonal twice the short side means angles of triangle are fixed. Now the question is triangle can be as big as possible or as small as possible.

Diagonal 4 more than the shorter side makes sure that there is only one triangle out of the unlimited ones from (1).

If half rectangle is known, full is known.

HTH, or ask again, I would try to explain more.
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Is the perimeter of a rectangle bigger than 8 inches? 1. the 17 Oct 2007, 11:57
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First the setup: perimeter > 8?

x = short side, y = long side, z = diagonal
2x + 2y > 8?
2(x+y) > 8?

[ x+y > 4? ]

1. x^2 + y^2 = (2x)^2
x^2+y^2 = 4x^2
y^2 = 3x^2

No numbers given, NOT SUFF.

2. z = x + 4

since x,y,z is a triangle we know that x+y > z
x + y > z
x + y > x + 4
x + y > x + 4 > 4

x + y > 4, SUFF.

Ans: B
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Is the perimeter of a rectangle bigger than 8 inches? 1. the 17 Oct 2007, 12:00
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Hyperstorm
First the setup: perimeter > 8?

x = short side, y = long side, z = diagonal
2x + 2y > 8?
2(x+y) > 8?

[ x+y > 4? ]

1. x^2 + y^2 = (2x)^2
x^2+y^2 = 4x^2
y^2 = 3x^2

No numbers given, NOT SUFF.

2. z = x + 4

since x,y,z is a triangle we know that x+y > z
x + y > z
x + y > x + 4
x + y > x + 4 > 4

x + y > 4, SUFF.

Ans: B
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Agree! B it is.

great explanation by hyperstorm! Forgot about triangle sides properties...
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Is the perimeter of a rectangle bigger than 8 inches? 1. the 17 Oct 2007, 15:47
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i would agree with B as well..

just did some approximation..

assume we have a triangle. where the diagonal of hte rectangular is the hyp of the right angle triangle..

(x+4)^2=x^2+y^2

where y is the other side...

you expand the expression you get

y=sqrt(8x+16)

now if assume x=1/8 then

y=sqrt(17) which means y approx equals 4...as you can see clearly the perimeter is going to be longer than 8...

worst case not possible but to try..x=0...
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Is the perimeter of a rectangle bigger than 8 inches? 1. the 17 Oct 2007, 18:14
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B.

(1) - diagonal could be .2, short side could be .1 ... or it could also be 200 and 100, INSUFFICIENT

(2) - The hypotenuse is less than the sum of the two other sides of a triangle. If the hypotenuse is 4 greater than the shorter side, the shorter side is .0001, the hypotenuse is 4.0001, and the longer side is > 4, which implies that the perimeter is .0001 + .0001 + >4 + >4 which is >8
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Is the perimeter of a rectangle bigger than 8 inches? 1. the 18 Oct 2007, 13:46
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The shortcut explained by Club is perimeter > sum of diagonals

the OA is B
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Is the perimeter of a rectangle bigger than 8 inches? 1. the 18 Oct 2007, 14:13
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bmwhype2
The shortcut explained by Club is perimeter > sum of diagonals

the OA is B
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P = 2 (L +W)

Two sides of a triangle must be larger than the 3rd side.

In essence, the perimeter is two sets of a length and a width. So 2 sets of L+W must be larger than 2 diagonals (the 3rd side).



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