The value of x is 20.
Solution:
Sides of one triangle are 2x – 4 and 39.
Sides of another triangle are x + 6 and 24.
Property of similar triangle:
If two triangles are similar then their corresponding angles are congruent and the corresponding sides are in the same ratio.
[tex]$\frac{2x-4}{24} =\frac{39}{x+6}[/tex]
Do cross multiplication.
[tex](2x-4)(x+6)=39\times 24[/tex]
[tex]2x^2+12x-4x-24=936[/tex]
[tex]2x^2+8x-24-936=0[/tex]
[tex]2x^2+8x-960=0[/tex]
Divide by 2 on each of the term.
[tex]x^2+4x-480=0[/tex]
Solve using quadratic equation.
[tex](x-20)(x+24)=0[/tex]
[tex](x-20)=0, \ (x+24)=0[/tex]
[tex]x = 20, \ x = -24[/tex]
Ignore the negative term, because if you substitute this you will get a negative terms only. But length of sides cannot be in negative measures.
Therefore x = 20.
