Question

A parallelogram has sides with lengths of `18` and `4`. If the parallelogram's area is `36`, what is the length of its longest diagonal?

Answer 1

Length of longest diagonal is `21.56` units.

Explanation:

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 `18` and `4` and area is `36` we have

`18xx4xxsintheta=36` or `sintheta=36/(18xx4)=1/2`

Hence `theta=30^@` and two angles of parallelogram are `30^@` and `150^@`.

Then smaller diagonal of parallelogram would be given by

`sqrt(a^2+b^2-2abcos30^@)=sqrt(18^2+4^2-2xx18xx4xx(sqrt3/2)`

= `sqrt(324+16-72xxsqrt3)=sqrt215.2923=14.67`

and larger diagonal of parallelogram would be given by

`sqrt(a^2+b^2-2abcos150^@)=sqrt(18^2+4^2+2xx18xx4xx(sqrt3/2)`

= `sqrt(324+16+72xxsqrt3)=sqrt464.7077=21.56`