Question

What are all of the values?

Answer 1

(i) x = 3

(ii) y = 6

Step-by-step explanation:

The two polygons are similar.

The congruent angles are:

∠J ≅ ∠G

∠R ≅ ∠M

∠I ≅ ∠A

∠C ≅ ∠T

∠E ≅ ∠H

Proportional sides are:

`(JR)/(GM) = (RI)/(MA) = (IC)/(AT) = (CE)/(TH) = (EJ)/(HG)`

(i) Value of x = ?

`(JR)/(GM) = (RI)/(MA)`

Putting the values from the figure

`(6)/(12) = (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 = ?

`(JR)/(GM) = (IC)/(AT)`

On putting the value we get:

`(6)/(12) = (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`