x is [tex]\frac{2y + 1}{2y - 3}[/tex]
Explanation:
Given:
EP = FP
GQ = FQ
Since the sides are equal, the ΔFPQ and ΔFEG are similar.
According to the property of similarity:
[tex]\frac{FP}{PE} =\frac{FQ}{QG}[/tex]
On substituting the value:
[tex]\frac{2x}{4y+2} = \frac{3x-1}{4y + 4} \\\\2x ( 4y + 4) = (3x-1)(4y+2)\\\\8xy + 8x = 12xy + 6x - 4y - 2\\\\4xy - 6x - 4y - 2 = 0\\\\2xy - 3x - 2y - 1 = 0\\\\2xy - 3x = 2y + 1\\\\x(2y - 3) = 2y +1\\\\x = \frac{2y+1}{2y-3}[/tex]
Perimeter will be sum of all the sides. If y is known then substitute the value and then find the perimeter.
