Question

A parallelogram has sides with lengths of `15` and `12`. If the parallelogram's area is `18`, what is the length of its longest diagonal?

Answer 1

Length of the longest diagonal is `15.05`

Explanation:

Let l = length = 15 & b = breadth = 12.
Area of parallelogram is l.h where h is the height.
`Area = l.h=15*h=18`
`:. h = 18/15 = 1.2`

Let d1 & d2 be the diagonals where in d1 is the longest.
`d1^2=l^2+h^2=15^2+1.2^2=225+1.44=226.44`
`color(red)(d1=15.05)`

For finding shortest diagonal:
`Aea`bh1=12h1=18# #h1=18/12=1.5#

Length of shortest diagonal `d2=sqrt(12^2+1.5^2)=sqrt(144+2.25)`
`color(green)(d2=12.1)`