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Square ABCD has an area of 9 square inches. Sides AD and BC

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Square ABCD has an area of 9 square inches. Sides AD and BC [#permalink]

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New post Updated on: 01 Aug 2012, 03:47
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Square ABCD has an area of 9 square inches. Sides AD and BC are lengthened to x inches each. By how many inches were sides AD and BC lengthened?
Attachment:
Square.png
Square.png [ 5.13 KiB | Viewed 6155 times ]


(1) The diagonal of the resulting rectangle measures 5 inches.
(2) The resulting rectangle can be cut into three rectangles of equal size.

Can anyone help me vvith B please .. Ive got A right

Originally posted by venmic on 31 Jul 2012, 20:11.
Last edited by Bunuel on 01 Aug 2012, 03:47, edited 1 time in total.
Added the diagram.
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Re: Square ABCD has an area of 9 square inches. [#permalink]

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New post Updated on: 01 Aug 2012, 00:40
Edit: never mind I thought it was a rectangle instead of a square, deleted my post to avoid confusion, I keep my explanation of statement 2 since it is mentioned by someone else below.


2) Any rectangle can be divided into 3 rectangles of equal size, insufficient

Originally posted by duriangris on 31 Jul 2012, 23:01.
Last edited by duriangris on 01 Aug 2012, 00:40, edited 1 time in total.
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Re: Square ABCD has an area of 9 square inches. [#permalink]

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New post 31 Jul 2012, 23:50
1
2
(1) Given that the area of the square is 9, then each side of the square is 3.
The lengthened sides will be of length 3 + x each, and the diagonal of the obtained rectangle being 5,
we can write \((x+3)^2+3^2=5^2\), from which \((x+3)^2=16\), so \(x = 1\).
Sufficient.

(2) Obviously, not sufficient, as was already mentioned by "duriangris" in the previous post.

Answer A.
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Re: Square ABCD has an area of 9 square inches. [#permalink]

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New post 01 Aug 2012, 00:38
EvaJager wrote:
(1) Given that the area of the square is 9, then each side of the square is 3.
The lengthened sides will be of length 3 + x each, and the diagonal of the obtained rectangle being 5,
we can write \((x+3)^2+3^2=5^2\), from which \((x+3)^2=16\), so \(x = 1\).
Sufficient.

(2) Obviously, not sufficient, as was already mentioned by "duriangris" in the previous post.

Answer A.

Gosh! it was a square not a rectangle!! :lol:
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Re: Square ABCD has an area of 9 square inches. Sides AD and BC [#permalink]

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New post 30 Jul 2016, 11:34
venmic wrote:
Square ABCD has an area of 9 square inches. Sides AD and BC are lengthened to x inches each. By how many inches were sides AD and BC lengthened?
Attachment:
Square.png


(1) The diagonal of the resulting rectangle measures 5 inches.
(2) The resulting rectangle can be cut into three rectangles of equal size.

Can anyone help me vvith B please .. Ive got A right

(1)-let side will be stretched x inches then side BC=3+x
so by pythagoras theorem
(3+x)^2+3^2=5^2
thus we can find x
suff...
(2) let BC be extended 6 inches then we have identical three 3*3 sized rectangle
But if BC extended 12 inches then also we get identical three 3*5 sized rectangle

insuff..
Ans A
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Re: Square ABCD has an area of 9 square inches. Sides AD and BC [#permalink]

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New post 31 Dec 2016, 03:42
If the square has an area of 9 square inches, it must have sides of 3 inches each. Therefore, sides AD and BC have lengths of 3 inches each. These sides are lengthened to x inches, while the other two remain at 3 inches. This gives us a rectangle with two opposite sides of length x and two opposite sides of length 3. Then we are asked by how much the two lengthened sides were extended. In other words, what is the value of x – 3? In order to answer this, we need to find the value of x itself.

(1) SUFFICIENT: If the resulting rectangle has a diagonal of 5 inches, we end up with the following:
We can now see that we have a 3-4-5 right triangle, since we have a leg of 3 and a hypotenuse (the diagonal) of 5. The missing leg (in this case, x) must equal 4. Therefore, the two sides were each extended by 4 – 3 = 1 inch.

(2) INSUFFICIENT: It will be possible, no matter what the value of x, to divide the resulting rectangle into three smaller rectangles of equal size. For example, if x = 4, then the area of the rectangle is 12 and we can have three rectangles with an area of 4 each. If x = 5, then the area of the rectangle is 15 and we can have three rectangles with an area of 5 each. So it is not possible to know the value of x from this statement.
The correct answer is A.
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Re: Square ABCD has an area of 9 square inches. Sides AD and BC [#permalink]

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New post 05 Sep 2017, 16:30
venmic wrote:
Square ABCD has an area of 9 square inches. Sides AD and BC are lengthened to x inches each. By how many inches were sides AD and BC lengthened?
Attachment:
Square.png


(1) The diagonal of the resulting rectangle measures 5 inches.
(2) The resulting rectangle can be cut into three rectangles of equal size.

Can anyone help me vvith B please .. Ive got A right


There is an alternative formula we can use to approach area of square problems- the square of diagonal divided by 2 equals the area of the square.

Statement 1

Yes because you could just square 5 and divide by 2 to get the area of the square which would give you the length of the sides of the new triangle

Statement 2

No because this is just saying the resulting side length has to be divisible by 3

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Re: Square ABCD has an area of 9 square inches. Sides AD and BC [#permalink]

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New post 08 Feb 2018, 12:23
Hi All

We're told that a square has an area of 9, so we know its sides all equal 3. We're told two opposite sides of the square are lengthened. We're asked how much they're lengthened.

1) The diagonal of the resulting rectangle is 5.

With this Fact, we'll have a rectangle with a side of 3, a side of X and a diagonal of 5. Since the diagonal 'cuts' the rectangle into two right triangles, we can determine the value of X - we'll have a 3/4/5 right triangle, so X MUST be 4 and the two side lengths were each lengthened by 1.
Fact 1 is SUFFICIENT

2) The resulting rectangle can be cut into three rectangles of equal size.

It's important to keep in mind that this Fact does NOT state that the dimensions of those 3 rectangles have to be integers nor does it tell us how we're supposed to 'cut' the rectangle (lengthwise or widthwise).

For example, draw a rectangle that is 3x4 and another that is 3x6. Now cut each of those rectangles into 3 smaller, equal rectangles. You'll see that each rectangle can be cut in two possible ways and that there's more than one possible end result, so the increase in side lengths can be any value.
Fact 2 is INSUFFICIENT

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Re: Square ABCD has an area of 9 square inches. Sides AD and BC [#permalink]

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New post 12 Feb 2018, 08:26
venmic wrote:
Square ABCD has an area of 9 square inches. Sides AD and BC are lengthened to x inches each. By how many inches were sides AD and BC lengthened?
Attachment:
Square.png


(1) The diagonal of the resulting rectangle measures 5 inches.
(2) The resulting rectangle can be cut into three rectangles of equal size.

Can anyone help me vvith B please .. Ive got A right


Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since the square ABCD has an area of 9 square inches. sides AD and BC are 3 inches. The question asks for the value of x - 3 because AD and BC are lengthened to x inches each.

Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
By Pythagoras theorem, since x^2 + 3^2 = 5^2, we have x = 4.
Condition 1) is sufficient on its own.

Condition 2)
Whatever the lengthes of sides of a rectangle are, all rectangles can be cut into three rectangles of equal size.
The condition 2) is not sufficient.

Therefore, the answer is A)

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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Re: Square ABCD has an area of 9 square inches. Sides AD and BC   [#permalink] 12 Feb 2018, 08:26
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