Question

A parallelogram has sides with lengths of `18` and `5`. If the parallelogram's area is `36`, what is the length of its longest diagonal?

Answer 1

Longest diagonal of the parallelogram is `20.55`

Explanation:

Area of a parallelogram whose sides are `a` and `b` and included angle `theta` is `axxbxxsintheta`

Hence, in the given instance `18xx5xxsintheta=36`

or `sintheta=36/(18xx5)=0.40`

Longest diagonal `L` of the parallelogram will be given by cosine formula

`L=sqrt(a^2+b^2+2abcostheta)`

As `costheta=sqrt(1-0.4^2)=sqrt0.84`

Hence, `L=sqrt(18^2+5^2+2xx18xx5xxsqrt0.84)`

= `sqrt(324+25+180xx0.9165)=sqrt(349+73.32)=sqrt422.32=20.55`

Smaller diagonal would be `S=sqrt(18^2+5^2-2xx18xx5xxsqrt0.84)=sqrt(349-73.32)=16.60`