A parallelogram has sides with lengths of #7 # and #16 #. If the parallelogram's area is #14 #, what is the length of its longest diagonal?

Answer 1

Longest diagonal has a length of approximately #22.96# units

the height #color(blue)(h = 2)#
#color(white)("XXXXXXXXX")#since base #xx# height #= 14#

The extension of the side with length #7# to a point perpendicularly below the furthest point of the diagonal
has a length given by the Pythagorean Theorem as
#color(white)("XXX")color(red)(x=sqrt(16^2-2^2) =sqrt(252))#

The length of the base plus the extension is
#color(white)("XXX")7+color(red)(sqrt(252))~~22.87#

By the Pythagorean Theorem, the longest diagonal,
#color(white)("XXX")color(green)(d)=sqrt(22.87^2+color(blue)(2)^2)~~22.96#

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Answer 2

Parker Allen

Using the formula for the area of a parallelogram, A = base * height, and knowing that the area is given as 14, we can solve for the height:

14 = 7 * h h = 2

Using the Pythagorean theorem, where the longest diagonal is the hypotenuse, we can find its length:

Longest diagonal = √(7² + 2² + 16²) = √(49 + 4 + 256) = √309 ≈ 17.58 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.