SOLUTION: In the diagram, BE= 45cm and AC=DC. Find the length of BC, in cm. Diagram: https://ibb.co/ThHHTr4

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Question 1148506: In the diagram, BE= 45cm and AC=DC. Find the length of BC, in cm.
Diagram: https://ibb.co/ThHHTr4
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
From your diagram,
let h=AC=DC
let x=BC
and then 45-x=CE.

Two right triangles. You want to find BC, or x.

system%2818%5E2%2Bx%5E2=h%5E2%2C%2845-x%29%5E2%2B20%5E2=h%5E2%29

18%5E2%2Bx%5E2=%2845-x%29%5E2%2B20%5E2------------simplify and solve for x.

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x be the length of BC.  Then the length of CE is (45-x).


From the condition, you have this equation


   18^2 + x^2 = (45-x)^2 + 20^2,


saying that the two hypotenuses have equal lengths.


Simplify and find x


    18^2 + x^2 = 45^2 - 90x + x^2 + 20^2

    90x        = 45^2 + 20^2 - 18^2

    90x        = 2101

      x        = 2101%2F90 = 23.344...   centimeters.     ANSWER

Solved.