x = 27, x = 3
Solution:
Figure (1):
If two triangles are similar, then the angles are congruent and the corresponding sides are proportional.
[tex]$\Rightarrow\frac{x+8}{2x-5} =\frac{10}{14}[/tex]
Do cross multiplication.
[tex]$\Rightarrow14(x+8)=10(2x-5)[/tex]
[tex]$\Rightarrow14x+112=20x-50[/tex]
Subtract 112 from both side of the equation.
[tex]$\Rightarrow14x+112-112=20x-50-112[/tex]
[tex]$\Rightarrow14x=20x-162[/tex]
Subtract 20x from both side of the equation.
[tex]$\Rightarrow14x-20x=20x-162-20x[/tex]
[tex]$\Rightarrow-6x=-162[/tex]
Divide by –6 on both sides.
⇒ x = 27
Figure (2):
If two triangles are similar, then the angles are congruent and the corresponding sides are proportional.
[tex]$\Rightarrow\frac{3}{4} =\frac{2.25}{x}[/tex]
[tex]$\Rightarrow3x=4\times2.25[/tex]
[tex]$\Rightarrow3x=9[/tex]
Divide by 3 on both sides of the equation.
[tex]$\Rightarrow\frac{3x}{3} =\frac{9}{3}[/tex]
⇒ x = 3
