SOLUTION: The sides of a right angled triangle are such that the sum of the length of the longest and that of the shortest side is twice the length of remaining side, the longest side of t

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Question 1207560: The sides of a right angled triangle are such that the sum of the length of the
longest and that of the shortest side is twice the length of remaining side, the
longest side of the triangle if the longer of the sides containing the right
angle is 9 CM more than half the hypotenuse is??
Found 5 solutions by greenestamps, josgarithmetic, Edwin McCravy, mccravyedwin, MathTherapy:
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


With no punctuation, your post is grammatically indecipherable....

Re-post, presenting the problem clearly.
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
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The sides of a right angled triangle are such that the sum of the length of the longest and that of the shortest side is twice the length of remaining side, the longest side of the triangle if the longer of the sides containing the right angle is 9 CM more than half the hypotenuse is??
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Trying to see the sections of description:
--
The sides of a right angled triangle are such that the sum of the length of the longest and that of the shortest side is twice the length of remaining side,
--


--
the longest side of the triangle if the longer of the sides containing the right angle is 9 CM more than half the hypotenuse is??
--


Maybe one attempt:
SIDES            LENGTH
leg               a
leg               b
hypotenuse        c

assuming ; and understood hypotenuse c is the longer side.



and

and the Pythagoream Theorem Formula gives .
Enough to work with.
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!

Answer by mccravyedwin(406)   (Show Source): You can put this solution on YOUR website!
The sides of a right angled triangle are such that the sum of the length of the
longest and that of the shortest side is twice the length of remaining side, what
is the length of the longest side of the triangle if the longer of the sides
containing the right angle is 9 CM more than half the hypotenuse is??

Let the length of the hypotenuse (the longest side) be x.
Let the length of the shortest side be y.
Then the length of the remaining side is 











 

 



What's under the radicals must be equal







So 

Now the sides of the right triangle are:

The length of the hypotenuse (the longest side) is x.
The length of the shortest side is 
Then the length of the remaining side is 





Since the longer of the sides containing the right
angle is 9 CM more than half the hypotenuse,






So the hypotenuse is 30 cm in length.



Edwin
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!
The sides of a right angled triangle are such that the sum of the length of the
longest and that of the shortest side is twice the length of remaining side, the
longest side of the triangle if the longer of the sides containing the right
angle is 9 CM more than half the hypotenuse is??

I agree with Sir Edwin's interpretation.

Let length of the LONGEST side (Hypotenuse) be H, the shortest side, S, and the middle side, M
                                           We then get: H + S = 2M
                                      But, it's given that 
                                So, H + S = 2M becomes:  

             We now have the lengths of all 3 sides as: 
As this is a right-angled triangle, we have:   
                        4H2 - H2 - 36H - 1,620 = 0 ----- Multiplying by LCD, 4
                             3H2 - 36H - 1,620 = 0 
                             3(H2 - 12H - 540) = 3(0) 
                                H2 - 12H - 540 = 0 
                              (H - 30)(H + 18) = 0
                                        H - 30 = 0          OR        H + 18 = 0 ==> H (Hypotenuse) = - 18 (IGNORE)
Length of longest side (HYPOTENUSE), or H = 30 cm
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