Answer:
The value of x is [tex]\frac{45}{4}[/tex]
Step-by-step explanation:
Property of similar triangle:
The ratio of the areas of two similar triangles is equal to the ratio of their corresponding sides.
Let us first label the points, angles and sides in the triangle (figure-1 )
and now re-draw the three similar triangles in a separate (figure-2)
We can find x by the ratio of their corresponding sides of first two triangle;
[tex]\frac{\,side\,opposite\,to\,angle\,a\,}{hypotenuse}=\frac{x}{15}=\frac{15}{20}[/tex]
[tex]\frac{x}{15}=\frac{3}{4}[/tex]
Multiply both the side by '15'
[tex]\x=\frac{3}{4}\times15[/tex]
[tex]\x=\frac{45}{4}[/tex]
Hence, the value of x is [tex]\frac{45}{4}[/tex]
