Question

The diagram represents the area of a rectangle as 9x2 + 24x + 16 square units.

What are the length and width of the rectangle in terms of x?
both:  3x + 4 units
both:  3x + 8 units
width: 3x + 4 units; length: 6x + 12 units
width: 3x + 8 units; length: 6x + 8 units

Answer 1

the correct answer is

A. both: 3x + 4 units

Explanation:

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Answer 2

we know that

A trinomial is a perfect square trinomial if it can be factored into a binomial multiplied to itself

so

`(a^(2) +2ab+b^(2))=(a+b)^(2)`

in this problem we have

`9x^(2) +24x+16`

both
`9x^(2)` and
`16` are perfect squares

hence

`9x^(2) +24x+16=(3x+4)^(2)`

`Length=(3x+4)\ units`

`Width=(3x+4)\ units`

therefore

the answer is

both: 3x + 4 units