Answer:
[tex]x=12,\ y=12[/tex]
Step-by-step explanation:
[tex]\text{Use the similar triangles concept.}\\\angle\text{B}=\angle\text{CDE because they both are marked with same symbol.}[/tex]
[tex]\text{Solution:}[/tex]
[tex]1.\ \text{In triangles ABC and CDE,}\\\text{i. }\angle\text{B}=\angle\text{CDE}\hspace{1cm}\text{(A)}\hspace{1cm}[\text{Given.}]\\\text{ii. }\angle\text{C}=\angle\text{C}\hspace{1.4cm}\text{(A)}\hspace{1cm}\text{[Common angle of both triangles.]}\\\text{iii. }\triangle\text{ABC}\sim\triangle\text{CDE}\hspace{0.15cm}\text{(A)}\hspace{1cm}\text{[By A.A. axiom]}[/tex]
[tex]\text{2. }\\\\\dfrac{\text{CE}}{\text{AC}}=\dfrac{\text{DE}}{\text{AB}}=\dfrac{\text{\text{CD}}}{\text{CB}}\hspace{0.2cm}\text{[Corresponding sides of similar triangles are proportional.]}[/tex]
[tex]\text{or, }\dfrac{24}{48}=\dfrac{y}{24}=\dfrac{18}{x+24}\\[/tex]
[tex]\text{or, }\dfrac{1}{2}=\dfrac{y}{24}=\dfrac{18}{x+24}[/tex]
[tex]\text{Taking first and second ratios, }\\\dfrac{1}{2}=\dfrac{y}{24}\\\\\text{or, }y=12[/tex]
[tex]\text{Taking the first and third ratios,}\\\dfrac{1}{2}=\dfrac{18}{x+24}\\\\\text{or, }x+24=36\\\text{or, }x=12[/tex]
