Question

Given EP = FP and GQ = FQ, what is the perimeter of ΔEFG?

Answer 1

x is  $\frac{2y + 1}{2y - 3}$

Explanation:

Given:

EP = FP

GQ = FQ

Since the sides are equal, the ΔFPQ and ΔFEG are similar.

According to the property of similarity:

$\frac{FP}{PE} =\frac{FQ}{QG}$

On substituting the value:

$\frac{2x}{4y+2} = \frac{3x-1}{4y + 4} \\\\2x ( 4y + 4) = (3x-1)(4y+2)\\\\8xy + 8x = 12xy + 6x - 4y - 2\\\\4xy - 6x - 4y - 2 = 0\\\\2xy - 3x - 2y - 1 = 0\\\\2xy - 3x = 2y + 1\\\\x(2y - 3) = 2y +1\\\\x = \frac{2y+1}{2y-3}$

Perimeter will be sum of all the sides. If y is known then substitute the value and then find the perimeter.