Home > Geometry > Quadrilaterals

A parallelogram has sides with lengths of #12 # and #4 #. If the parallelogram's area is #36 #, what is the length of its longest diagonal?

Answer 1

Savannah Aguilar

The length of the longest diagonal is #=sqrt(160+24sqrt7)#

We have a parallelogram #ABCD#

#AD=4#

#AB=12#

Area = base x height

#36=12*h#

#h=3#

The distance between the base of the height and the corner #D# is

#=sqrt(AD^2-h^2)=sqrt(16-9)=sqrt7#

Therefore,

#DB^2=h^2+(DC+sqrt7)#

#DB^2=9+(12+sqrt7)^2#

#DB^2=9+144+7+24sqrt7#

#DB^2=160+24sqrt7#

#DB=sqrt(160+24sqrt7)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Allison Allen

To find the length of the longest diagonal of the parallelogram, you can use the formula for the area of a parallelogram, which is given by the product of the length of one side and the corresponding altitude.

Given that the area is 36 and one side has a length of 12, the altitude must be 3.

Now, use the Pythagorean theorem to find the length of the longest diagonal.

Let (d) be the length of the longest diagonal. Then, using the sides of the parallelogram and the altitude, we have:

(d^2 = 12^2 + 3^2)

(d^2 = 144 + 9)

(d^2 = 153)

(d = \sqrt{153})

Thus, the length of the longest diagonal of the parallelogram is (\sqrt{153}).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.