A parallelogram has sides with lengths of #14 # and #15 #. If the parallelogram's area is #63 #, what is the length of its longest diagonal?

Answer 1

Find the height, then use Pythagoras in two different right-angled triangles to get the length of the longer diagonal
#d =28.66#

Draw a sketch of the parallelogram first, extend the base and draw in the height to meet the extended base. There are two right-angled triangles formed.

Find the height of the parallelogram. A = b x h

#h = A/b = 63/15 = 21/5 = 4.2#

The endpoint of the top line of the parallelogram is vertically above the base extended. We need to calculate the length of the extended line, let's call it #x#.

Working in the right-angled triangle outside the parallelogram with Hypotenuse = 14 and height = 4.2, gives the following:

#x^2 = 14^2 -4.2^2 = 178.36# #x = sqrt178.36 " "# leave it in this form

Length of the extended base = #15 + sqrt178.36~~28.355#

Now work with the right-angled triangle with the longer diagonal# (d)# as the hypotenuse, and the two shorter sides being #4.2 and (15+sqrt178.36)#

#d^2 = (15+sqrt178.36)^2 +4.2^2 =821.654....#

#d = 28.66#

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Answer 2

Maverick Smith

The length of the longest diagonal of the parallelogram is 19.

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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.