Given two similar triangles
The corresponding sides are proportions
So,
[tex]\frac{x}{y}=\frac{24}{42}=\frac{4}{7}[/tex]So, the relation between x and y will be:
[tex]x=\frac{4}{7}y[/tex]The area of the smaller triangle = 42 cm^2
So, area =
[tex]\frac{1}{2}x\cdot y=42[/tex]Substitute with x into the equation of the area to find the value of y
[tex]\begin{gathered} \frac{1}{2}\cdot\frac{4}{7}y\cdot y=42 \\ \\ y^2=\frac{42\cdot2\cdot7}{4}=\frac{588}{4}=147 \\ y=\sqrt[]{147} \end{gathered}[/tex]Substitute with y into x
[tex]x=\frac{4}{7}\cdot\sqrt[]{147}=\frac{4\sqrt[]{147}}{7}[/tex]So, the answer will be:
[tex]\begin{gathered} x=\frac{4\sqrt[]{147}}{7} \\ \\ y=\sqrt[]{147} \end{gathered}[/tex]