Question

Find the length of the height of the right trapezoid shown below, if it has the greatest possible area and its perimeter is equal to 6 units.

Answer 1

1

Explanation:

i dont know the explaination sorry but the answer should be correct

Answer 2

The height of the right trapezoid is
`(6)/(5+√(3))\ units`

Explanation:

Let

x ----> the height of the right trapezoid in units

we know that

The perimeter of the figure is equal to

`P=AB+BC+CD+DH+HA`

we have

`P=6\ units`

`AB=BC=CH=HA=x` ---> because is a square

substitute

`6=x+x+CD+DH+x`

`6=3x+CD+DH` -----> equation A

In the right triangle CDH

`sin(30\°)=(CH)/(CD)`

`sin(30\°)=(1)/(2)`

so

Remember that
`CH=x`

`(1)/(2)=(x)/(CD)`

`CD=2x`

`tan(30\°)=(CH)/(DH)`

`tan(30\°)=(√(3))/(3)`

so

`(√(3))/(3)=(x)/(DH)`

`DH=x√(3)`

substitute the values in the equation A

`6=3x+CD+DH` -----> equation A

`CD=2x`

`DH=x√(3)`

`6=3x+2x+x√(3)`

`6=5x+x√(3)`

`6=x[5+√(3)]`

`x=(6)/(5+√(3))\ units`