Given:
[tex]\Delta ABC\sim \Delta D EF[/tex]
[tex]AB=15,BC=y,AC=18,DE=12,EF=9,DF=x[/tex]
To find:
The values of x and y.
Solution:
We have,
[tex]\Delta ABC\sim \Delta D EF[/tex]
Corresponding sides of similar triangles are proportional.
[tex]\dfrac{AB}{DE}=\dfrac{BC}{EF}=\dfrac{AC}{DF}[/tex]
On substituting the values, we get
[tex]\dfrac{15}{12}=\dfrac{y}{9}=\dfrac{18}{x}[/tex]
[tex]\dfrac{5}{4}=\dfrac{y}{9}=\dfrac{18}{x}[/tex]
Now,
[tex]\dfrac{5}{4}=\dfrac{y}{9}[/tex]
[tex]\dfrac{5}{4}\times 9=\dfrac{y}{9}\times 9[/tex]
[tex]\dfrac{45}{4}=y[/tex]
[tex]11.25=y[/tex]
And
[tex]\dfrac{5}{4}=\dfrac{18}{x}[/tex]
[tex]5\times x=18\times 4[/tex]
[tex]x=\dfrac{72}{5}[/tex]
[tex]x=14.4[/tex]
Therefore, the value of x is 14.4 units and value of y is 11.25 units.
