Question

1. if lo = 15x + 19 and qn = 10x + 2, find pn.

d ad.

1. find m∠ade

Explanation:

Step1: Use rectangle diagonal property

In a rectangle, diagonals bisect each other, so $LO = PN$ and $QN = QP$. Also, the segments of the diagonals are equal: $LO = 2 \times QN$
$15x + 19 = 2(10x + 2)$

Step2: Solve for x

Expand and simplify the equation:
$15x + 19 = 20x + 4$
$19 - 4 = 20x - 15x$
$15 = 5x$
$x = 3$

Step3: Calculate QN length

Substitute $x=3$ into $QN = 10x + 2$:
$QN = 10(3) + 2 = 32$

Step4: Find PN length

$PN = 2 \times QN$
$PN = 2 \times 32 = 64$

Answer:

64