Question

A parallelogram has a base of length `(2x+1)` and a height of `(x+3)` and has an area of 42 square units. Find the base and height of the parallelogram?

Answer 1

There are two solutions - base b=6 and height h=7 or b=7 and h=6.

Explanation:

conditions from the question:
`b = 2x + 1, h = x + 3, bh = 42`
hence
`(2x + 1)(x+3) = 42`
`2x^2 + 6x + x + 3 - 42 = 0`
`2x^2 + 7x - 39 = 0`

Solving quadratic equation:
`Delta = 49 + 4 * 2 * 39 = 361=19^2`
so the roots are:
`x = (-7 ± 19)/4 in {3, -13/2}`

Substituting each root to b and h gives a solution:
`x = 3 Rightarrow b = 7, h = 6`
`x = -13/2 Rightarrow b = -12, h = -7/2`