Question

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

Explanation:

Using a side of length `7` as the base
`color(white)("XXX")`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`