Instead of walking along two adjacent sides of a rectangular field, Sa

Question

Instead of walking along two adjacent sides of a rectangular field, Sabrina took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side is:

(A) 1:4
(B) 3:8
(C) 1:2
(D) 2:3
(E) 3:4

(A) 1:4 
(B) 3:8 
(C) 1:2 
(D) 2:3 
(E) 3:4

sagarsir · Answer

Preferably look for an option that has diagonal as integer and test t. OPTION E 3,4,5. Saving = 3+4-5=2 which is half the longer side 4. Kudos... If you like

King407 · Answer

d = (l+b) - l/2  and  d = \sqrt{(l^2*b^2)}

=> (2l + 2b - l) = 2d => l+2b = 2d => (l+2b)^2 = 4(l^2+b^2) => l^2+4b^2+4lb = 4l^2+4b^2 => 3l^2 = 4lb => b:l = 3:4

Hence answer is E

sanguine2016 · Answer

Let l and b be the two sides of rectangular field. Diagonal will be \sqrt{ l^2 + b^2 }.
It is given that::
 \sqrt{ l^2 + b^2 } =  (l+b) - l/2 
Now Squaring both the sides we get,
=> l^2 + b^2  = ( l/2 + b)^2 
=>  l^2 + b^2  = ((l^2)/4 + b^2 + lb) 
=>  (l) * ((3/4)l -b)  =  0 
=>  ((3/4)l -b)  = 0 
=>  b/l  =  3/4 
Hence, E Answer.

EMPOWERgmatRichC · Answer

Hi All,

There's a great 'pattern-matching' shortcut in this question that is something you'll likely see on Test Day. Spotting the pattern can save you LOTS of time on this question...

Since the diagonal of a rectangle forms right triangles within the rectangle AND the answer choices are INTEGERS, it's quite likely that the right triangles will be one of the Classic Pythagorean Triples: 3/4/5 or 5/12/13 (although there are other, rarer, possibilities). If you notice that one of the answers fits one of those patterns, then you can go straight to that answer and check to see if it "fits" the rest of the information in the question. You'll see that it DOES fit and you've got the answer.

GMAT assassins aren't born, they're made,
Rich

gleizzable1 · Answer

Let L be the longer side
Let w bebthe short side

It says that the path where she made a short cut saved half of the longer sider. So we can say

1/2 L + W

Using phytagorean theorem we have

L^2 + W^2 = (1/2 L + W)^2
L^2 + W^2 = 1/4 L^2 + WL + W^2

Combining like terms we have

3/4 L^2 = WL 
Divide both side with L
3/4 L = W

Ratio will be 3/4 = W/L

KarishmaB · Answer

Your logic makes perfect sense that you should check for integral diagonal first though note one thing - the actual length of the diagonal NEED NOT be an integer. For example, the actual sides could be 1.5 and 2 such that the diagonal is 2.5 and sum of 1.5 + 2/2 is also 2.5. The sum of one side + half of another side may not be an integer and hence the diagonal may not be an integer.
What is important is that the diagonal must be a  RATIONAL  number.

For example, if we test for option (A) 1:4
The diagonal of the rectangle with sides 1 and 4 would be  \sqrt{17} . That is an irrational number. This is not possible since the sum of 1 + 4/2 = 3 will be rational. 
Only in case of option (E) will we get a RATIONAL diagonal length = 5.
Hence option (E) is correct.

vijay556 · Answer

Diagonal = (Length + Breadth)- Length / 2
Diagonal = 1/2 * Length + Breadth
4(l^2+b^2) = l^2+4b^2+4lb
3l^2=4lb
b/l=3/4

E

JeffTargetTestPrep · Answer

We can let D = the diagonal, S = the shorter side and L = the longer side. From the information in the problem, we see that:

S + L = D + L/2

S + L/2 = D

Furthermore, we can use the Pythagorean theorem:

S^2 + L^2 = D^2

If we square the equation S + L/2 = D, we have:

(S + L/2)(S + L/2) = D^2

S^2 + L^2/4 + SL = D^2

Substituting D^2 by S^2 + L^2, we have:

S^2 + L^2/4 + SL = S^2 + L^2

SL = 3L^2/4

4SL = 3L^2

4S = 3L

S/L = 3/4

Answer: E

bumpbot · Answer

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Instead of walking along two adjacent sides of a rectangular field, Sa

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