Question 1087043
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Two smaller right-angled triangles are similar, which gives the proportion

{{{(8-x)/y}}} = {{{x/(6-y)}}}.


It implies

(8-x)*(6-y) = xy,

48 - 6x - 8y + xy = xy,

48 = 6x + 8y,

3x + 4y = 24.


So, you have these two equations

3x + 4y = 24,    (1)   and
xy = 12.         (2)


From (1), express x = {{{(24 - 4y)/3}}} and substitute it into (2). You will get

a quadratic equation, which you can easily solve (by any method you know).


I will leave the details to you.


<U>Answer</U>.  x = 4 cm, y = 3 cm.
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