Question

What are all of the values?

Answer 1

(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:

$\frac{JR}{GM} = \frac{RI}{MA} = \frac{IC}{AT} = \frac{CE}{TH} = \frac{EJ}{HG}$

(i) Value of x = ?

$\frac{JR}{GM} = \frac{RI}{MA}$

Putting the values from the figure

$\frac{6}{12} = \frac{2x + 1}{3x + 5} \\\\6 ( 3x + 5) = 12 ( 2x + 1)\\\\18x + 30 = 24x + 12\\\\30 - 12 = 24x - 18x\\\\18 = 6x\\\\x = 3$

(ii) Value of y = ?

$\frac{JR}{GM} = \frac{IC}{AT}$

On putting the value we get:

$\frac{6}{12} = \frac{x^2-4}{y+4} \\\\6(y+4) = 12(x^2 - 4)\\\\6y + 24 = 12[(3)^2 - 4]\\\\6y + 24 = 12[ 9 - 4]\\\\6y + 24 = 60\\\\6y = 36\\\\y = 6$