Answer:
[tex] x = 7 [/tex]
Step-by-step explanation:
since the corresponding respective sides of a similar triangles are proportional.
Using this fact:
we can say that
[tex] \sf \dfrac{KJ}{MN} = \dfrac{JL}{MP} [/tex]
Now, substitute the given values:
[tex] \dfrac{25}{30} = \dfrac{20}{4x-4} [/tex]
Next, simplify the fractions:
[tex] \dfrac{5}{6} = \dfrac{20}{4x-4} [/tex]
Now, cross-multiply to eliminate the denominators:
[tex] 5(4x-4) = 6 \times 20 [/tex]
Distribute on the left side:
[tex] 20x - 20 = 120 [/tex]
Add 20 on both sides:
[tex] 20x - 20 +20= 120 +20[/tex]
[tex] 20x = 140 [/tex]
Divide both sides by 20.
[tex]\dfrac{20x}{20}=\dfrac{140}{20}[/tex]
[tex] x = 7 [/tex]
So, the value of [tex]x[/tex] is 7.
