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

Algebra.Com
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(39617)   (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.



------------simplify and solve for x.
Answer by ikleyn(52777)   (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        =  = 23.344...   centimeters.     ANSWER

Solved.


RELATED QUESTIONS

In the diagram, BE=45cm and AC=DC. Find the length of BC, in cm. Diagram:... (answered by josgarithmetic,ikleyn)
In the diagram, BE = 45 cm and AC = DC . Find the length of BC, in cm.... (answered by mananth)
In the diagram, BE = 50 cm and AC=DC. Find the length of BC, in cm.... (answered by josgarithmetic)
In the diagram, Line BE=80 cm, and Line AC=Line DC. Find the length of Line BC, in cm. (answered by ikleyn,Alan3354)
In the diagram, AB = BC and BD=DC=CE. AB=4 cm. Find the length of AE, in cm.... (answered by ikleyn,math_tutor2020)
In the diagram below, Triangle ABC is isosceles, and Triangle MPQ is equilateral. Find... (answered by ikleyn,Edwin McCravy)
In the diagram, ABCG is a parallelogram, and BF = 18 cm, FE = 6 cm. Find the length, in... (answered by greenestamps)
(64) Triangle ABC has AD ⊥ BC and BE ⊥ AC. If AD = 20, BC = 29 and BE = 21, then find (answered by ikleyn)
In the diagram below, find the measure of Angle BFD. Diagram:... (answered by ikleyn)