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(13200) About Me  (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) About Me  (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??
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Trying to see the sections of description:
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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,
--


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

assuming a%3Cb; and understood hypotenuse c is the longer side.


a%2Bc=2b
and
b=9%2Bc%2F2
and the Pythagoream Theorem Formula gives a%5E2%2Bb%5E2=c%5E2.
Enough to work with.

Answer by Edwin McCravy(20055) About Me  (Show Source):
Answer by mccravyedwin(407) About Me  (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 sqrt%28x%5E2-y%5E2%29





x%2By%22%22=%22%222%2Asqrt%28x%5E2-y%5E2%29

x%2By%22%22=%22%222%2Asqrt%28%28x-y%29%28x%2By%29%29

x%2By%22%22=%22%222%2Asqrt%28x-y%29%2Asqrt%28x%2By%29%29

%28x%2By%29%2Fsqrt%28x%2By%29%22%22=%22%222%2Asqrt%28x-y%29 

sqrt%28x%2By%29%22%22=%22%22sqrt%284%29%2Asqrt%28x-y%29 

sqrt%28x%2By%29%22%22=%22%22sqrt%284%28x-y%29%29

What's under the radicals must be equal

x%2By%22%22=%22%224%28x-y%29

x%2By%22%22=%22%224x-4y

5y%22%22=%22%223x

So y%22%22=%22%22expr%283%2F5%29x

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 expr%283%2F5%29x
Then the length of the remaining side is 
sqrt%28x%5E2-y%5E2%29%22%22=%22%22sqrt%28x%5E2-%28expr%283%2F5%29x%29%5E2%29%22%22=%22%22sqrt%28x%5E2-expr%289%2F25%29x%5E2%29%22%22=%22%22sqrt%28expr%2816%2F25%29x%5E2%29%22%22=%22%22expr%284%2F5%29x




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

expr%284%2F5%29x%22%22=%22%22expr%281%2F2%29x%2B9
8x%22%22=%22%225x%2B90
3x%22%22=%22%2290
x%22%22=%22%2230

So the hypotenuse is 30 cm in length.



Edwin

Answer by MathTherapy(10552) About Me  (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 matrix%281%2C3%2C+M%2C+%22=%22%2C+H%2F2+%2B+9%29
                                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