Question

Suppose Evan is trying to build a frame out of popsicle sticks x inches long. The frame will have length (2x – 3) and width of (x – 2). If the popsicle sticks are 3 inches long, what is the area of the frame in inches and expressed as a polynomial? A. 3 square inches; 2x2 – 7x + 6 B. 3 square inches; 2x4 – 4x + 6 C. 21 square inches; 2x2 – x + 6 D. 15 square inches; 2x2 – 3x + 6

Answer 1

The correct option is A) 3 square inches;
`2x^2-7x+6`.

Explanation:

It is given that the length of the frame is (2x-3) and the width is (x-2)

The area of the rectangle is:
`A=l* w`

Where, A is the area l is the length and w is the width of the rectangle.

Put
`l=(2x-3)` and
`w=(x-2)` in the area of the rectangle.

`A=(2x-3)(x-2)\\A=2x^2-4x-3x+6\\A=2x^2-7x+6`

The area of the frame expressed as a polynomial is
`2x^2-7x+6`.

Now substitute x=3 in
`A=2x^2-7x+6`.

`A=2(3)^2-7(3)+6\\A=18-21+6\\A=3`

The area of the frame is 3 square inches.

Hence, the correct option is A) 3 square inches;
`2x^2-7x+6`.