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

Answer:

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

Step-by-step 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: $A=l\times w$

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; $2x^2-7x+6$.