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If p is the perimeter of rectangle Q, what is the value of [#permalink]

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08 Jul 2008, 23:17

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If p is the perimeter of rectangle Q, what is the value of p?

1. Each diagonal of rectangle Q has length 10

2. The area of rectangle Q is 48

---- Here's my question. Doesn't "(1) Each diagonal"... imply that 2 diagonals cross in a square and that you can assume equal lengths of 5 for each bisected side? Graphically... \ and / = X

If p is the perimeter of rectangle Q, what is the value of p?

1. Each diagonal of rectangle Q has length 10

2. The area of rectangle Q is 48

---- Here's my question. Doesn't "(1) Each diagonal"... imply that 2 diagonals cross in a square and that you can assume equal lengths of 5 for each bisected side? Graphically... \ and / = X

Thanks very much

answer to your question : yes each diagonal will bisect each other in a rectangle, but that doesn not mean that its a square. For it to be square, diagonals should bisect each other and andgle between them should be 90.

Now lest solve the question

if x and y are the two sides. we have to find out 2(x+y)

statement 1 : \([m]x^2 + y^2 = 100\)[/m] . there coudl be more than one possible solution for (x,y) not suff statement 2 : xy = 48, again not suff

combine : we know (x+y)^2 = x^2 + y^2 +2xy mean we can find out x+y... Suff

If p is the perimeter of rectangle Q, what is the value of p?

1. Each diagonal of rectangle Q has length 10

2. The area of rectangle Q is 48

---- Here's my question. Doesn't "(1) Each diagonal"... imply that 2 diagonals cross in a square and that you can assume equal lengths of 5 for each bisected side? Graphically... \ and / = X

Thanks very much

for 1) consider a rectangle of 8x6 or a square of length 10/sqrt(2), both have diagonal of 10 , but perimeters are different.

If p is the perimeter of rectangle Q, what is the value of p?

1. Each diagonal of rectangle Q has length 10

2. The area of rectangle Q is 48

---- Here's my question. Doesn't "(1) Each diagonal"... imply that 2 diagonals cross in a square and that you can assume equal lengths of 5 for each bisected side? Graphically... \ and / = X

Thanks very much

1. Rectangular has two diagonals which have the same length ==> the rectangular must be square. So the perimeter = 4*(10/2)*aqrt(2)

2. area = 48, hmm we can not determine the length and width of rectangular.

If p is the perimeter of rectangle Q, what is the value of p?

1. Each diagonal of rectangle Q has length 10

2. The area of rectangle Q is 48

---- Here's my question. Doesn't "(1) Each diagonal"... imply that 2 diagonals cross in a square and that you can assume equal lengths of 5 for each bisected side? Graphically... \ and / = X

Thanks very much

1. Rectangular has two diagonals which have the same length ==> the rectangular must be square. So the perimeter = 4*(10/2)*aqrt(2)

2. area = 48, hmm we can not determine the length and width of rectangular.

A is best answer.

Who say this -> Rectangular has two diagonals which have the same length ==> the rectangular must be square. ?

for 1) consider a rectangle of 8x6 or a square of length 10/sqrt(2), both have diagonal of 10 , but perimeters are different.

The square of length 10/sqrt(2) would not have an area of 48 - would be 50.

We are intersted in perimeter, not in area.

Above I was trying to say that since there are (atleast) 2 possibilities that the the rectangle can be a 8x6 rectangle or a square with side 10/sqrt(2), the perimeters will be different and thus 1) alone won't be suffcient.

If p is the perimeter of rectangle Q, what is the value of p?

1. Each diagonal of rectangle Q has length 10

2. The area of rectangle Q is 48

---- Here's my question. Doesn't "(1) Each diagonal"... imply that 2 diagonals cross in a square and that you can assume equal lengths of 5 for each bisected side? Graphically... \ and / = X

Thanks very much

p=2(a+b) ; a+b =?

1.sqrt(a^2+b^2) = 10 NS 2.ab= 48 NS from 1 and 2 we can solve for a and b