Answer:
[tex]x=1[/tex]
Step-by-step explanation:
Given:
Parallelogram P is dilated to form parallelogram P'.
The side of P which is = 10 units corresponds 20 units in P'.
The side of P which is given as =(x+3) units corresponds 8 units in P'.
To find the value of [tex]x[/tex].
Solution:
The scalar factor of dilation from P to P' can be given as the ratio of the corresponding sides of the parallelograms.
The scalar factor :
⇒ [tex]\frac{\textrm{Side on parallelogram P'}}{\textrm{Side on parallelogram P}}[/tex]
⇒ [tex]\frac{20}{10}[/tex]
⇒ 2
This means the sides of the parallelogram P' is twice the sides of the parallelogram P.
The side of P which is given as =(x+3) units corresponds 8 units in P'.
Using the scalar factor the equation to solve for [tex]x[/tex] can be given as:
⇒ [tex]2(x+3)=8[/tex]
Solving for [tex]x[/tex].
Using distribution:
⇒ [tex]2x+6=8[/tex]
Subtracting both sides by 6.
⇒ [tex]2x+6-6=8-6[/tex]
⇒ [tex]2x=2[/tex]
Dividing both sides by 2.
⇒ [tex]\frac{2x}{2}=\frac{2}{2}[/tex]
∴ [tex]x=1[/tex] (Answer)
