Problem with similar triangles

[branko917]

Another problem that i need help to solve.




The sum of two hypotenuses l1+l2=15

What is the value of x and y. I need in detail step by step problem solving solution.

Thanks.

 

[anon_hedgepig]

You have two similar triangles as you've noted.
You can form a ratio for the non-hypotenuse legs for the larger triangle and relate them to the smaller triangle. What do you get?

 

[branko917]

You have two similar triangles as you've noted.
You can form a ratio for the non-hypotenuse legs for the larger triangle and relate them to the smaller triangle. What do you get?

T tried that way, i get y=2xy-2x/10, x=10y-xy/y-2, from this a cant get clear ratio between x and y.

 

[Dr.Peterson]

T tried that way, i get y=2xy-2x/10, x=10y-xy/y-2, from this a cant get clear ratio between x and y.

Please use parentheses: you meant y=(2xy-2x)/10 and x=(10y-xy)/(y-2).

But that's not how you solve for x or y; you still have a variable on both sides. Given [MATH]2x+10y=2xy[/MATH], isolate one variable, like this: [MATH]2x = 2xy-10y[/MATH]; so [MATH]2x = 2(x-5)y[/MATH], and then solve for y. Then you will have y in terms of x.

Then you have another fact to use: [MATH]l_1+l_2=15[/MATH]. This initially looks ugly, but it will simplify greatly if you are careful.

 

[branko917]

Please use parentheses: you meant y=(2xy-2x)/10 and x=(10y-xy)/(y-2).

But that's not how you solve for x or y; you still have a variable on both sides. Given [MATH]2x+10y=2xy[/MATH], isolate one variable, like this: [MATH]2x = 2xy-10y[/MATH]; so [MATH]2x = 2(x-5)y[/MATH], and then solve for y. Then you will have y in terms of x.

Then you have another fact to use: [MATH]l_1+l_2=15[/MATH]. This initially looks ugly, but it will simplify greatly if you are careful.

Thank you, this was very helpfull.