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
The OA is the option E.
I liked this question, but I couldn't solve it. Which is the equation that we get from the statement? Experts, may you help me? Thanks in advanced.
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Instead of walking along two adjacent sides of
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Hi Vincen,
We're told that 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 of the longer side. We're asked for the ratio of the shorter side to the longer side. Rather than try to approach this with a complex series of calculations, you can take advantage of the 'patterns' that exist in math (especially in Geometry) and the Answer choices to TEST THE ANSWERS.
To start, we're clearly going to be dealing with a right triangle, so the Pythagorean Theorem (A^2 + B^2 = C^2) will come into play. When using this formula, it's important to realize that in MOST cases, the 3 values will NOT all be integers. Choose 2 random numbers for A and B and the likely result will be that C is a non-integer. Here though, we're told that walking the diagonal length of the field 'saves' EXACTLY HALF the length of the long side. Mathematically-Speaking, that would be....
A + B - (1/2)(B) = C where A is the short side, B is the long side and C is the diagonal
A + (1/2)(B) = C
This equation heavily implies that A, B and C are ALL going to be INTEGERS - and if you know the common Pythagorean Triplets (3/4/5 and 5/12/13), then there's a logical answer choice to test first....
Let's TEST Answer E..... 3:4
IF.... the short side is 3 and the long side is 4, then we'll have a 3/4/5 right triangle and the diagonal will be 5.
Here, the diagonal IS equal to the short side + 1/2 of the long side (re: 3 + (1/2)(4) = 3 + 2 = 5). This is an exact match for what we were told, so this MUST be the answer!
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
We're told that 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 of the longer side. We're asked for the ratio of the shorter side to the longer side. Rather than try to approach this with a complex series of calculations, you can take advantage of the 'patterns' that exist in math (especially in Geometry) and the Answer choices to TEST THE ANSWERS.
To start, we're clearly going to be dealing with a right triangle, so the Pythagorean Theorem (A^2 + B^2 = C^2) will come into play. When using this formula, it's important to realize that in MOST cases, the 3 values will NOT all be integers. Choose 2 random numbers for A and B and the likely result will be that C is a non-integer. Here though, we're told that walking the diagonal length of the field 'saves' EXACTLY HALF the length of the long side. Mathematically-Speaking, that would be....
A + B - (1/2)(B) = C where A is the short side, B is the long side and C is the diagonal
A + (1/2)(B) = C
This equation heavily implies that A, B and C are ALL going to be INTEGERS - and if you know the common Pythagorean Triplets (3/4/5 and 5/12/13), then there's a logical answer choice to test first....
Let's TEST Answer E..... 3:4
IF.... the short side is 3 and the long side is 4, then we'll have a 3/4/5 right triangle and the diagonal will be 5.
Here, the diagonal IS equal to the short side + 1/2 of the long side (re: 3 + (1/2)(4) = 3 + 2 = 5). This is an exact match for what we were told, so this MUST be the answer!
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
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We can let D = the diagonal, S = the shorter side and L = the longer side. From the information in the problem, we see that:Vincen wrote: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
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
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