Question

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

d = 28, find ad.

1. find m∠ade.

Explanation:

Step1: Use rectangle diagonal property

In rectangle \(LPON\), diagonals bisect each other, so \(LO = 2QN\)
\(15x + 19 = 2(10x + 2)\)

Step2: Solve for \(x\)

Expand and simplify:
\(15x + 19 = 20x + 4\)
\(19 - 4 = 20x - 15x\)
\(15 = 5x\)
\(x = 3\)

Step3: Calculate \(QN\)

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

Step4: Find \(PN\)

Diagonals of rectangle are equal, \(PN = LO = 2QN\)
\(PN = 2\times32 = 64\)

Answer:

\(64\)