Question

A parallelogram has sides with lengths of `16` and `15`. If the parallelogram's area is `60`, what is the length of its longest diagonal?

Answer 1

Length of the longer diagonal `d=30.7532" "`units

Explanation:

The required in the problem is to find the longer diagonal `d`

Area of the parallelogram `A=base * height=b*h`
Let base `b=16`
Let other side `a=15`
Let the height `h=A/b`

Solve for height `h`
`h=A/b=60/16`

`h=15/4`

Let `theta` be the larger interior angle which is opposite the longer diagonal `d`.

`theta=180^@-sin^-1 (h/a)=180^@-14.4775^@`
`theta=165.522^@`

By the Cosine Law, we can solve now for `d`

`d=sqrt((a^2+b^2-2*a*b*cos theta))`
`d=sqrt((15^2+16^2-2*15*16*cos 165.522^@))`
`d=30.7532" "`units

God bless....I hope the explanation is useful.