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# Triangular region T1

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Triangular region T1 [#permalink]  14 Dec 2016, 01:59
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Question Stats:

53% (01:06) correct 46% (00:41) wrong based on 13 sessions
Triangular region T1 and T2 have equal areas and have heights h1 and h2 respectively

 Quantity A Quantity B $$\frac{(area of T1)}{h1}$$ $$\frac{area of T2)}{h2}$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: Triangular region T1 [#permalink]  29 Dec 2016, 14:34
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Expert's post
Carcass wrote:
Triangular region T1 and T2 have equal areas and have heights h1 and h2 respectively

 Quantity A Quantity B (area of T1)/h1 (area of T2)/h2

Area of a triangle = (base)(height)/2

Let b1 = length of base of T1
So, area of T1 = (b1)(h1)/2

Let b2 = length of base of T2
So, area of T2 = (b2)(h2)/2

We get:
Quantity A: [(b1)(h1)/2]/h1
Quantity B: [(b2)(h2)/2]/h2

Simplify to get:
Quantity A: (b1)/2
Quantity B: (b2)/2

Multiply both quantities by 2 to get:
Quantity A: b1
Quantity B: b2

Since we aren't told anything about the lengths of the two bases, there's no way to determine which is bigger.

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Re: Triangular region T1 [#permalink]  29 Dec 2016, 14:43
Expert's post
Carcass wrote:
Triangular region T1 and T2 have equal areas and have heights h1 and h2 respectively

 Quantity A Quantity B (area of T1)/h1 (area of T2)/h2

Another approach is to look at different cases.

Area of a triangle = (base)(height)/2

case 1:
T1 has base of 4 and a height (h1) of 4
T2 has base of 4 and a height (h2) of 4

Area of T1 = (4)(4)/2 = 8
Area of T2 = (4)(4)/2 = 8
As you can see the two triangles have the same area.

We get:
Quantity A: (area of T1)/h1 = 8/4 = 2
Quantity B: (area of T2)/h2 = 8/4 = 2
In this case, the the two quantities are equal

case 2:
T1 has base of 4 and a height (h1) of 3
T2 has base of 3 and a height (h2) of 4

Area of T1 = (4)(3)/2 = 6
Area of T2 = (3)(4)/2 = 6
As you can see the two triangles have the same area.

We get:
Quantity A: (area of T1)/h1 = 6/3 = 2
Quantity B: (area of T2)/h2 = 6/4 = 1.5
In this case, the quantity A is greater

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Brent Hanneson – Creator of greenlighttestprep.com

Re: Triangular region T1   [#permalink] 29 Dec 2016, 14:43
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