## ILoveComputers1 one year ago a=x, b=x, c=50 solve for x (hint: this is an isosceles triangle)

1. anonymous

is 50 supposed to be one of the angles?

2. ILoveComputers1

They give me a triangle, and it's showing the pythagorean theorem. So it is finding the sides not angles.

3. anonymous

|dw:1439787827242:dw| Like this?

4. ILoveComputers1

Yes just like that. |dw:1439787916367:dw|

5. anonymous

well then just us Pythagrian theorem

6. anonymous

x^2 + x^2 = 50^2 solve for x

7. nincompoop

start by the definition of isosceles that two sides of the triangle have equal length. if that is our unknown, then the third side would be 50

8. nincompoop

|dw:1439788089504:dw|

9. ILoveComputers1

So then I would get 2x^2= 50^2 x^2=25^2 x=25

10. nincompoop

|dw:1439788184602:dw|

11. nincompoop

|dw:1439788232741:dw|

12. nincompoop

we utilize a few algebraic acrobat using a few formulas like the pythagorean theorem but we must recognize that there is now a fourth side and perhaps we can use simpler formula to solve for x

13. nincompoop

one of these suggestion is to bisect the side with length 50 instead of x and it may be easier to work with, because of known facts that come with it |dw:1439788720560:dw|

14. nincompoop

Let me redraw |dw:1439788819981:dw|

15. nincompoop

we are following the constraints or clue that our triangle is an isosceles so we will use isosceles right triangle :D

16. nincompoop

$$\large \sqrt{a^2 + b^2 } =c \rightarrow \sqrt{x^2 + x^2} = c = \sqrt{2x^2}$$ $$\large \sqrt{2x^2}= 50$$ the rest of the solutions are easy to work with