Question

1. if efgh is an isosceles trapezoid. eh = 4x - 27, fg = x + 9, eg = 3y + 19, and fh = 11y - 21. solve for x and y.

Explanation:

Step1: Set legs equal (isosceles trapezoid)

$4x - 27 = x + 9$

Step2: Solve for x

$4x - x = 9 + 27$
$3x = 36$
$x = \frac{36}{3} = 12$

Step3: Set diagonals equal (isosceles trapezoid)

$3y + 19 = 11y - 21$

Step4: Solve for y

$19 + 21 = 11y - 3y$
$40 = 8y$
$y = \frac{40}{8} = 5$

Answer:

$x = 12$
$y = 5$