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The length of one of the sides of a triangle is 25 units. If the area

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The length of one of the sides of a triangle is 25 units. If the area  [#permalink]

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New post Updated on: 04 Nov 2018, 08:33
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The length of one of the sides of a triangle is 25 units. If the area of the triangle is 120 units^2 and the length of the another side of the triangle is 10 units. Find the length of the third side.
A) \(\sqrt{255}\)
B) \(\sqrt{585}\)
C) \(\sqrt{572}\)
D) \(\sqrt{558}\)
E) 24

Weekly Quant Quiz #7 Question No 7


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Originally posted by gmatbusters on 03 Nov 2018, 10:14.
Last edited by gmatbusters on 04 Nov 2018, 08:33, edited 1 time in total.
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Re: The length of one of the sides of a triangle is 25 units. If the area  [#permalink]

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New post 03 Nov 2018, 10:59
USing pythagoras theorem ans E
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Re: The length of one of the sides of a triangle is 25 units. If the area  [#permalink]

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New post 03 Nov 2018, 11:05
The length of one of the sides of a triangle is 25 units. If the area of the triangle is 120 units^2 and the length of the another side of the triangle is 10 units. Find the length of the third side.

so lets say a = 25, b =10 and area = 120

so 3rd side cannot be greater than 35 (sum of 2 sides) and also should be at least greater than 15 as (>15+10 ) will be greater than side being 25

area of triangle = 1/2 * side * perpendicular

E cannot be the solution as we know 1/2*24*10 becomes 120 but it has to be right angled triangle which does not satisfies Pythagorus theorem. (AB^2+BC^2= AC^2)

area calculation possibility = 1/2 * side *25 or 1/2*side *10

option A: sqrt (255) close to 16 as 16 square is 256 hence 1/2*16*25= 120
option B: sqrt (585) is greater than 24 and hence none of the area calculation possibility fits here
Option C: sqqrt(572) is less than 24 and hence none of the area calculation possibility fits here
option D: sqrt (558) is less than 24 and hence does not fit any of the area calculation possibility

hence A is the answer
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Re: The length of one of the sides of a triangle is 25 units. If the area  [#permalink]

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New post 03 Nov 2018, 12:19
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Given -

base*height = 240, other side = 25

Let Base = 10, Height = 24.

Now, we have \(24^2 +7^2 = 25^2\)
So, the perpendicular will be at distance of 7 from side with length 25.

Length of other side = \(24^2 + 3^2\) = 585
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Re: The length of one of the sides of a triangle is 25 units. If the area  [#permalink]

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New post 03 Nov 2018, 13:00
root585
Herons Formula s=(35+c)/2
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Re: The length of one of the sides of a triangle is 25 units. If the area  [#permalink]

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New post 04 Nov 2018, 02:37
1
Area of ABC = 1/2 * 25 * AD = 120

AD = 9.6

BD^2 = 100 - 92.16 = 7.84
BD = 2.8

DC = 22.2

AC = 22.2^2 + 9.6^2
=√585
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Re: The length of one of the sides of a triangle is 25 units. If the area  [#permalink]

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New post 13 Nov 2018, 12:54
Hi fskilnik,

I have a doubt in this problem.
why can the 3rd side not be 24? (somebody mentioned above that it is a right triangle and hence the 3rd side cannot be 24. my doubt is why do we consider the triangle to right triangle when it is not mentioned in the question)
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Re: The length of one of the sides of a triangle is 25 units. If the area  [#permalink]

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New post 13 Nov 2018, 13:03
yashna36 wrote:
Hi fskilnik,

I have a doubt in this problem.
why can the 3rd side not be 24? (somebody mentioned above that it is a right triangle and hence the 3rd side cannot be 24. my doubt is why do we consider the triangle to right triangle when it is not mentioned in the question)

Hi, yashna36!

In any triangle (right triangle or not), each side must be greater than the difference of the other two, and less than the sum of the other two.

When you have three potential sides (I mean, side lengths), it is enough to check whether the greater length is less than the sum of the other two:

25 < 10+24 guarantees there exists a triangle with 10, 24 and 25 as its lengths.

To know whether this 10, 24, 25 triangle is right, just check whether 25^2 = 24^2 + 10^2. The answer is NO, hence this triangle is not a right triangle.

I hope you got things clearer.

Regards,
Fabio.
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Re: The length of one of the sides of a triangle is 25 units. If the area  [#permalink]

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New post 14 Nov 2018, 08:25
1
Quote:
The length of one of the sides of a triangle is 25 units. If the area of the triangle is 120 units squared and the length of another side of the triangle is 10 units, which of the following could be the length of the third side?
A) \(\sqrt{255}\)
B) \(\sqrt{585}\)
C) \(\sqrt{572}\)
D) \(\sqrt{558}\)
E) 24

\(? = x\)

Image

\(\left\{ \begin{gathered}
\,{x^2} = {\left( {10 + 7} \right)^2} + {24^2} = 289 + 576\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,x = \sqrt {865} \hfill \\
\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{OR}} \hfill \\
\,{x^2} = {24^2} + {3^2} = 576 + 9\,\,\,\, \Rightarrow \,\,\,\,x = \sqrt {585} \hfill \\
\end{gathered} \right.\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: The length of one of the sides of a triangle is 25 units. If the area   [#permalink] 14 Nov 2018, 08:25
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