A parallelogram has sides with lengths of #16 # and #5 #. If the parallelogram's area is #48 #, what is the length of its longest diagonal?

Answer 1

Length of its longest diagonal is #20.22#

Area of a parallelogram is given by #axxbxxsintheta#,
where #a# and #b# are two sides of a parallelogram and #theta# is the angle included between them.
As sides are #16# and #5# and area is #48# we have
#16xx5xxsintheta=48# or #sintheta=48/(16xx5)=3/5#
#costheta=sqrt(1-(3/5)^2)=sqrt(1-9/25)#
= #sqrt(16/25)=4/5#

Then larger diagonal of parallelogram would be given by

#sqrt(a^2+b^2-2abcosthet)=sqrt(16^2+5^2+2xx16xx5xx4/5#
= #sqrt(256+25+128)=sqrt409#
= #20.22#
Sign up to view the whole answer

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

Sign up with email
Answer 2

To find the length of the longest diagonal of a parallelogram, you can use the formula:

[ \text{Area} = \text{Base} \times \text{Height} ]

For a parallelogram, the base can be any of its sides. Let's assume the side of length 16 as the base and the side of length 5 as the height. Therefore, we have:

[ 48 = 16 \times \text{Height} ]

Solving for the height:

[ \text{Height} = \frac{48}{16} = 3 ]

Now, to find the length of the longest diagonal, you can use the Pythagorean theorem, since the diagonals of a parallelogram bisect each other:

[ \text{Longest diagonal} = \sqrt{16^2 + (2 \times \text{Height})^2} ]

Substituting the values:

[ \text{Longest diagonal} = \sqrt{16^2 + (2 \times 3)^2} = \sqrt{256 + 36} = \sqrt{292} ]

Therefore, the length of the longest diagonal of the parallelogram is ( \sqrt{292} ).

Sign up to view the whole answer

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

Sign up with email
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.

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.

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.

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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7