Question

8
g 8x - 19 h
2x + 5
j
f i
*fh = 20
find hi
find gj

Explanation:

Step1: Set GH equal to FI (parallelogram opposite sides)

$8x - 19 = 2x + 5$

Step2: Solve for x

$8x - 2x = 5 + 19$
$6x = 24$
$x = \frac{24}{6} = 4$

Step3: Find length of GJ (diagonals bisect)

$GJ = \frac{1}{2} \times FH$
$GJ = \frac{1}{2} \times 20 = 10$

Step4: Find length of HI (opposite to FG)

$HI = FG = 2x + 5$
$HI = 2(4) + 5 = 8 + 5 = 13$

Answer:

$GJ = 10$, $HI = 13$