(i) x = 3
(ii) y = 6
Explanation:
The two polygons are similar.
The congruent angles are:
∠J ≅ ∠G
∠R ≅ ∠M
∠I ≅ ∠A
∠C ≅ ∠T
∠E ≅ ∠H
Proportional sides are:
[tex]\frac{JR}{GM} = \frac{RI}{MA} = \frac{IC}{AT} = \frac{CE}{TH} = \frac{EJ}{HG}[/tex]
(i) Value of x = ?
[tex]\frac{JR}{GM} = \frac{RI}{MA}[/tex]
Putting the values from the figure
[tex]\frac{6}{12} = \frac{2x + 1}{3x + 5} \\\\6 ( 3x + 5) = 12 ( 2x + 1)\\\\18x + 30 = 24x + 12\\\\30 - 12 = 24x - 18x\\\\18 = 6x\\\\x = 3[/tex]
(ii) Value of y = ?
[tex]\frac{JR}{GM} = \frac{IC}{AT}[/tex]
On putting the value we get:
[tex]\frac{6}{12} = \frac{x^2-4}{y+4} \\\\6(y+4) = 12(x^2 - 4)\\\\6y + 24 = 12[(3)^2 - 4]\\\\6y + 24 = 12[ 9 - 4]\\\\6y + 24 = 60\\\\6y = 36\\\\y = 6[/tex]
