Question 1207560
<pre>
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(1,3, M, "=", H/2 + 9)}}}
                                So, H + S = 2M becomes: {{{matrix(3,3, H + S, "=", 2(H/2 + 9), H + S, "=", H + 18, S, "=", 18)}}} 

             We now have the lengths of all 3 sides as: {{{matrix(3,3, H, "=", Hypotenuse, 18, "=", S, H/2 + 9, "=", M)}}}
As this is a right-angled triangle, we have: {{{matrix(4,3, H^2, "=", 18^2 + (H/2 + 9)^2, H^2, "=", 324 + (H/2)^2 + 2(9)(H/2) + 9^2, H^2, "=", 324 + H^2/4 + 9H + 81, H^2 - H^2/4 - 9H - 405, "=", 0)}}}  
                        4H<sup>2</sup> - H<sup>2</sup> - 36H - 1,620 = 0 ----- Multiplying by LCD, 4
                             3H<sup>2</sup> - 36H - 1,620 = 0 
                             3(H<sup>2</sup> - 12H - 540) = 3(0) 
                                H<sup>2</sup> - 12H - 540 = 0 
                              (H - 30)(H + 18) = 0
                                        H - 30 = 0          OR        H + 18 = 0 ==> H (Hypotenuse) = - 18 (IGNORE)
<font color = red><font size = 4><b>Length of longest side</font></font></b> (HYPOTENUSE), or H = <font color = red><font size = 4><b>30 cm</font></font></b></pre>