The length of the CD is approximately equal to 26.
Pythagorean theorem
Using the Pythagorean theorem,
The Pythagoras theorem equation exists expressed as, [tex]c^{2} = a^{2} + b^{2}[/tex], where 'c' be the hypotenuse of the right triangle and 'a' and 'b' exists the other two legs.
To find BA:
Where, BA = [tex]$\sqrt{37^{2}+53^{2}}=\sqrt{4178}$[/tex]
Consider BC = x,
To find the length of [tex]$B D: \sqrt{x^{2}+37^{2}}$[/tex]
Since DBA exists in a right triangle,
[tex]$D A^{2}=B D^{2}+B A^{2}$[/tex]
Substitute the values in the above equation, and we get
[tex]$(x+53)^{2}=\sqrt{4178}^{2}+{\sqrt{x^{2}+37^{2}}}^{2}$[/tex]
Expanding the above equation, we get
[tex]$x^{2}+106 x+2809=x^{2}+5547$[/tex]
Simplifying the equation,
106x = 2736
Divide 2736 by 106, and we get
x = 25.8 approximately 26.
Therefore, the length of the CD is approximately equal to 26.
To learn more about the Pythagorean theorem,
https://brainly.com/question/20545047
#SPJ2
