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0
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PLS READ CAREFULLY BC THERE IS A SIMILAR PROBLEM

A right triangle with integer leg lengths is called cool if the number of square units in its area is equal to twice the number of units in the sum of the lengths of its legs. What is the sum of all the different possible areas of cool right triangles?

Jan 2, 2023

#1
+1

2(x + y) = 1/2*x*y

4x + 4y - xy = 0

4x + y(4 - x) = 0

y = 4x/(x - 4)

Therefore, x > 4, y  > 4 since x and y must both be positive.

the only positive integer x values that give positive integer y values are    5,6,8,12,and 20

But i just realized that is not what you asked.

(5,20)    area = 0.5*5*20 = 50

(6,12)    area = 0.5*6*12 = 36

(8,8)      area = 0.5*8*8  = 32

(12,6)    area  is 36

(20,5)    area is 50

so sum of all possible areas is   50+36+32 = 118 units squared.

Jan 2, 2023
#2
+660
0

Its not right, sorry. Thank you, but can someone still HELP!!!!

Keihaku  Jan 2, 2023
#3
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If an an answer is wrong then state why you know this and if possible find the error.

Also, and if it is a genuine attempt at help as this one appears to be, say thanks (which you did  )  then give them a point for their interest and time.

Also, if an question has been asked before, no matter how wrong or ablsent the answers may be, give a link to the original question and request that people answer on the original and ask answerers then leave a note on the repost saying that they have answered.

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Melody  Jan 2, 2023
edited by Melody  Jan 2, 2023
edited by Melody  Jan 2, 2023
#4
0

I assume that when you say "legs" you mean the 3 sides of the triangle. If that is so, then:

I can find only 1 such right triangle:

9^2  +  40^2 = 41^2

Area = (9 x 40) / 2 = 180 u^2

Sum of its 3 sides = 9 + 40 + 41 = 90 u

So, the area is 2 times the sum of the 3 sides of the triangle.

Jan 2, 2023