Answer:
C
Step-by-step explanation:
Using the Pythagorean theorem, find BA: [tex]\sqrt{37^{2}+53^{2} } = \sqrt{4178}[/tex]
Making BC = x, find the lenth of BD: [tex]\sqrt{x^{2} +37^{2} }[/tex]
Since DBA is a right triangle, this follows: [tex]DA^{2}=BD^{2}+BA^{2}[/tex]
Substitute: [tex](x+53)^{2} =\sqrt{4178} ^{2} +\sqrt{x^2+37^2} ^{2}[/tex]
Expand: [tex]x^{2} +106x+2809=x^{2} +5547[/tex]
Solve: 106x = 2736
Finally: x ≈ 25.8 ≈ 26
Therefore: C
