Answer:
The value of x is 5 cm
Step-by-step explanation:
we can see that there are two triangles
smaller triangle and larger triangle
and both triangles are similar
so, the ratio of their sides must be equal
we get
[tex]\frac{x}{x+30}=\frac{4}{4+24}[/tex]
now, we can solve for x
[tex]\frac{x}{x+30}=\frac{4}{28}[/tex]
we can cross multiply
[tex]x\left(4+24\right)=\left(x+30\right)\cdot \:4[/tex]
[tex]28x=4x+120[/tex]
Subtract both sides by 4x
[tex]28x-4x=4x+120-4x[/tex]
[tex]24x=120[/tex]
Divide both sides by 24
[tex]\frac{24x}{24}=\frac{120}{24}[/tex]
[tex]x=5[/tex]
