Janelle drew KL in isosceles trapezoid FGHJ to create similar trapezoids FKLJ and KGHL. Based on the given information, what are the values of y and w in centimeters?

w = 36 centimeters

y = 24 centimeters

Step-by-step explanation:

The exact question is as follows :

Given - Janelle drew KL in isosceles trapezoid FGHJ to create similar trapezoids FKLJ and KGHL.

To find - Based on the given information, what are the values of y and w in centimeters?

Solution -

We can see that from the diagram,

Trapezoid FKLJ is 3 times bigger than Trapezoid KGHL

So,

The side KL = 3 times side GH

⇒12 = 3×4

⇒12 = 12 centimeters

So,

side FJ = 3 times side KL

⇒w = 3×12

⇒w = 36 centimeters

Now,

The side KF = 3 times side KG

⇒KF = 3×8

⇒KF = 24

Now,

We know,

In  isosceles trapezoid  two opposite sides (the bases) are parallel, and the two other sides (the legs) are of equal length

So,

Side LJ = side KF

⇒y = 24 centimeters

∴ we get

w = 36 centimeters

y = 24 centimeters