Question

The area of a rectangle is represented by the expression 2x2 + 10x + 12. Daniel is convinced that the dimensions of this rectangle could be (2x + 4) and (x + 3) or (x + 2) and (2x + 6). Do you agree or disagree with Daniel? Use words to justify your opinion.

Answer 1

I agree with daniel

Explanation:

Given the area of a rectangle expressed as;

A(x) = 2x²+10x+12

On factorizing;

A(x) = 2x²+6x+4x+12

A(x) = 2x(x+3)+4(x+3)

A(x) = (x+3)(2x+4)

since A(x) = l(x)w(x)

Hence the legnth and width of the rectangle are 2x+4 and x+3.

Also A(x) = 2x²+6x+4x+12 can be factorized as;

A(x) = 2x²+4x+6x+12

A(x) = 2x(x+2) + 6(x+2)

A(x) = 2x+6(x+2)

Therefore I agree with Daniel. The factor differs due to the difference in arrangement of 4x and 6x in the expression. Precedence of values affects the final factors