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A parallelogram has sides with lengths of #16 # and #9 #. If the parallelogram's area is #54 #, what is the length of its longest diagonal?

Answer 1

Autumn Armstrong

Length of its longest diagonal is #24.576#

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 #9# and area is #54# we have

#16xx9xxsintheta=54# or #sintheta=54/(16xx9)=3/8#

#costheta=sqrt(1-(3/8)^2)=1/8sqrt55=0.927#

Then larger diagonal of parallelogram would be given by

#sqrt(a^2+b^2-2abcos150^@)=sqrt(16^2+9^2+2xx16xx9xx0.927#

= #sqrt(256+81+288xx0.927)=sqrt(337+266.976)#

= #sqrt603.976=24.576#

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Answer 2

Sophia Alfred

The length of the longest diagonal of the parallelogram is 17 units.

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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.