Question

Given: ABCD is a rhombus AC = 3x + 1, and BD = 4x + 2 The area of a rhombus can be represented by the formula A= 1 2 d1d2 where d1 and d2 are diagonals of the polygon. Which expression represents the area of the rhombus? \

Answer 1

There are no options to choose from so....
A = 6x^2 -x -1; factors to (2x -1)(3x + 1)
Hopefully this will be on the right track of the answers.

Answer 2

A = 6x² + 5x + 1

Explanation:

The area of a rhombus is
`A= (1)/(2) d_(1) d_(2)` where d₁ is one diagonal and d₂ is the other diagonal.

If we have the rhombus ABCD, the diagonals are AC and BD.

The problem tells us that AC = 3x + 1 and BD = 4x + 2

Substituting this in our formula for the area and simplifying as much as we can (by factorizing) we get:

`A= ((3x+1)(4x+2))/(2) \\2A= (3x+1)(4x+2)\\2A= 12x^(2) +10x+2\\2A = 2(6x^(2) +5x+1)\\2A=2(3x+1)(2x+1)\\A=(3x+1)(2x+1)`

Therefore the area is A = (3x + 1) (2x + 1). If you want to solve the parenthesis you'd get A = 6x² + 5x + 1