## anonymous one year ago HELP is anyone in connexus!!? geometry B and can help

1. DanJS

i did that polygon similarity one you closed

2. anonymous

@DanJS thank you Dan mind helping me again

3. DanJS

sure

4. anonymous

I need to find the value of x and y but im confused as to how

5. DanJS

first thing i see is just to set up 2 pythagorean theorems, and solve for x and y

6. DanJS

maybe, might be too much work

7. anonymous

im just confused im not sure how to get it

8. DanJS

Triangle ABC and Triangle BDC are similar, they both have 3 of the same angles

9. DanJS

since both have a right angle and the same marked angle, so the third angle is the same

10. DanJS

so you can do ratios of the sides like last prob

11. DanJS

$\frac{ AB }{ BD } = \frac{ BC }{ AC } = \frac{ BC }{ DC }$

12. DanJS

$\frac{ 5 }{ 3 } = \frac{ y }{ x+4 } = \frac{ y }{ x }$

13. DanJS

You can solve that for x and y

14. anonymous

can you show me how to?

15. anonymous

yes kinda

16. anonymous

Not gonna lie im a bit lost by that

17. DanJS

sorry that is false, i messed up

18. anonymous

oh lol okay

19. DanJS

ok, i just used two pythagorean theorems, and got x = 9/4 and y=15/4

20. DanJS

Solving 5^2 + y^2 = (4+x)^2 and 3^2 + x^2 = y^2

21. DanJS

did it on my calculator, no work

22. anonymous

Hmmm thank you dan :)

23. DanJS

welcome

24. mathstudent55

In a right triangle, if an altitude is drawn to the hypotenuse, then all three triangles are similar. This is the situation with this problem. Start with triangle ABC. Since angle ABC is a right angle, triangle ABC is a right triangle. Segment BD is the altitude of triangle ABC drawn to the hypotenuse of triangle ABC. That means that triangles ABC, ADB, and BDC are similar triangles. Once you know the triangles are similar, then the lengths of corresponding sides are proportional, so you can write these two proportions: $$\dfrac{AB}{BC} = \dfrac{AD}{BD}$$ and $$\dfrac{AD}{BD} = \dfrac{BD}{DC}$$ Replacing all segments by their given lengths, x, and y, you get: $$\dfrac{5}{y} = \dfrac{4}{3}$$ and $$\dfrac{4}{3} = \dfrac{3}{x}$$ $$4y = 15$$ $$4x = 9$$ $$y = \dfrac{15}{4} = 3.75$$ $$x = \dfrac{9}{4} = 2.25$$