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No need to be apologetic k4lnamja. You can ask any question so far it's related to the topic.
We are dealing with a right angle triangle;
We are given its area and the hypotenuse and we are asked for perimeter.
Right angle triangle has three sides; one of which is hypotenuse. If we know the length of the other two, we will have the perimeter. However, there is no way to find out the length of the other two sides individually. Thus, our intention is to find the combined length of the other two sides and add it up with the hypotenuse to get the perimeter.
How can we use the information to know the combined length of the other two sides. Here's how.
Hypotenuse = c = 12 Let the other two sides of the right angle triangle be "a" and "b" and we know these two sides are perpendicular to each other.
Area = 28 Area of a triangle = 1/2*base*height = 1/2*a*b
1/2*a*b=28 a*b=56 c=12
As per pythagoras: a^2+b^2=c^2 (a+b)^2-2ab=c^2 (a+b)^2-2*56=12^2 (a+b)^2-112=144 (a+b)^2=256 a+b=16
Thus, we know the sum of other two sides. a+b=16 c=12 a+b+c=16+12=28 ******************
Ans: "C"
********************** Just to expand the formula used: (a+b)^2=a^2+b^2+2ab (a+b)^2-2ab=a^2+b^2 (a+b)^2-2ab=c^2 ********************** _________________
Re: If a right triangle has area 28 and hypotenuse 12, what is [#permalink]
28 Jun 2015, 09:50
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Re: If a right triangle has area 28 and hypotenuse 12, what is [#permalink]
16 Aug 2015, 17:08
amit2k9 wrote:
1/2 * 12 * altitude = 28 altitude = 7
using similar triangle
7/x = x/12 gives x^2 = 84
12^2 - 84 = 60
thus 60 ^ (1/2) + 84 ^(1/2) + 12 = 28.7 approx.
Hence C.
I know it's been a long time since this post was made, but is anyone able to explain where 7/x = x/12 gives x^2 = 84 comes from??? I would like to try and understand this alternate approach that uses the hypotenuse as the base.
Thanks! _________________
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Re: If a right triangle has area 28 and hypotenuse 12, what is [#permalink]
16 Aug 2015, 17:12
Expert's post
DropBear wrote:
amit2k9 wrote:
1/2 * 12 * altitude = 28 altitude = 7
using similar triangle
7/x = x/12 gives x^2 = 84
12^2 - 84 = 60
thus 60 ^ (1/2) + 84 ^(1/2) + 12 = 28.7 approx.
Hence C.
I know it's been a long time since this post was made, but is anyone able to explain where 7/x = x/12 gives x^2 = 84 comes from??? I would like to try and understand this alternate approach that uses the hypotenuse as the base.
Thanks!
Cross-multiply \(\frac{7}{x} = \frac{x}{12}\) to get \(7*12=x*x\) --> \(84=x^2\). _________________
Re: If a right triangle has area 28 and hypotenuse 12, what is [#permalink]
16 Aug 2015, 17:20
Bunuel wrote:
DropBear wrote:
amit2k9 wrote:
1/2 * 12 * altitude = 28 altitude = 7
using similar triangle
7/x = x/12 gives x^2 = 84
12^2 - 84 = 60
thus 60 ^ (1/2) + 84 ^(1/2) + 12 = 28.7 approx.
Hence C.
I know it's been a long time since this post was made, but is anyone able to explain where 7/x = x/12 gives x^2 = 84 comes from??? I would like to try and understand this alternate approach that uses the hypotenuse as the base.
Thanks!
Cross-multiply \(\frac{7}{x} = \frac{x}{12}\) to get \(7*12=x*x\) --> \(84=x^2\).
Hi Bunuel,
Thanks for the very quick reply. I understand the calculation, just not sure about how we use similar triangles to arrive at that line in the first place? Don't understand why we are doing \(\frac{7}{x} = \frac{x}{12}\) in the first place... Sorry if this seems rudimentary... _________________
If you found my post useful, please consider throwing me a Kudos... Every bit helps
Re: If a right triangle has area 28 and hypotenuse 12, what is [#permalink]
16 Aug 2015, 17:24
DropBear wrote:
amit2k9 wrote:
1/2 * 12 * altitude = 28 altitude = 7
using similar triangle
7/x = x/12 gives x^2 = 84
12^2 - 84 = 60
thus 60 ^ (1/2) + 84 ^(1/2) + 12 = 28.7 approx.
Hence C.
I know it's been a long time since this post was made, but is anyone able to explain where 7/x = x/12 gives x^2 = 84 comes from??? I would like to try and understand this alternate approach that uses the hypotenuse as the base.
As a matter of fact, the text in red above is incorrect. The altitude should be 14/3 and NOT 7 as it has been calculated. The final answer as well is an integer, dont know how is the poster getting a decimal value.
IMO, the method is a 'forced' one as I am having difficulty in coming to the same equation for 'x'. Not a good method. _________________
If a right triangle has area 28 and hypotenuse 12, what is [#permalink]
16 Aug 2015, 17:50
Engr2012 wrote:
DropBear wrote:
amit2k9 wrote:
1/2 * 12 * altitude = 28 altitude = 7
using similar triangle
7/x = x/12 gives x^2 = 84
12^2 - 84 = 60
thus 60 ^ (1/2) + 84 ^(1/2) + 12 = 28.7 approx.
Hence C.
I know it's been a long time since this post was made, but is anyone able to explain where 7/x = x/12 gives x^2 = 84 comes from??? I would like to try and understand this alternate approach that uses the hypotenuse as the base.
As a matter of fact, the text in red above is incorrect. The altitude should be 14/3 and NOT 7 as it has been calculated. The final answer as well is an integer, dont know how is the poster getting a decimal value.
IMO, the method is a 'forced' one as I am having difficulty in coming to the same equation for 'x'. Not a good method.
I completely overlooked that part in red, in that case 1/2 * 12 * altitude = 28 altitude = 4 2/3. However I will take your advice and leave this one alone as I don't want to confuse myself.
Edit: Edited 4 3/2 to 4 2/3
_________________
If you found my post useful, please consider throwing me a Kudos... Every bit helps
Last edited by DropBear on 16 Aug 2015, 18:48, edited 1 time in total.
Re: If a right triangle has area 28 and hypotenuse 12, what is [#permalink]
16 Aug 2015, 18:46
DropBear wrote:
I completely overlooked that part in red, in that case 1/2 * 12 * altitude = 28 altitude = 4 3/2. However I will take your advice and leave this one alone as I don't want to confuse myself.
I believe you meant 4 2/3 instead of 4 3/2 _________________
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