SOLUTION: A rectangle has a 12 cm2 area is inside a right triangle, as shown in the image. <a rel=nofollow HREF="http://es.tinypic.com?ref=sp81g3" target="_blank"><img src="http://i67.ti

Algebra ->  Triangles -> SOLUTION: A rectangle has a 12 cm2 area is inside a right triangle, as shown in the image. <a rel=nofollow HREF="http://es.tinypic.com?ref=sp81g3" target="_blank"><img src="http://i67.ti      Log On


   

Question 1087043: A rectangle has a 12 cm2 area is inside a right triangle, as shown in the image.
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Calculate x and y.
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
Two smaller right-angled triangles are similar, which gives the proportion

%288-x%29%2Fy = x%2F%286-y%29.


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 = %2824+-+4y%29%2F3 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.


Answer.  x = 4 cm, y = 3 cm.