Question

Given:

Answer 1

Answer:

9 units

Step-by-step explanation:

By the midsegment theorem,

$AB=\dfrac{KN+LM}{2}$

Since the ratio $LM:KN=1:5,$ then $LM=x,\ KN=5x$ and

$18=\dfrac{x+5x}{2}\\ \\18=\dfrac{6x}{2}\\ \\18=3x\\ \\x=6\\ \\LM=6\ units\\ \\KN=30\ units$

Draw two heights LE and MF. Quadrilateral ELMF is a rectangle, then EF = LM = 6 units.

Trapezoid KLMN is isosceles trapezoid (KL = MN), then KE = FN and

$KE=FN=\dfrac{KN-EF}{2}=\dfrac{30-6}{2}=12\ units$

Consider right triangle KLE. By the Pythagorean theorem,

$KL^2=LE^2+KE^2\\ \\15^2=LE^2+12^2\\ \\LE^2=15^2-12^2\\ \\LE^2=225-144=81\\ \\LE=9\ units$