Question

I need help i don’t understand the questions are down below

Answer 1

A picture and a frame are given with dimensions. It is required to find the area of the frame.

To find the area of the frame, subtract the area of the picture from the total area (frame + picture).

Recall the area of a rectangle with a length l and a width w:

`A=l\cdot w`

Substitute l=22 and w=20 into the formula to find the area of the picture:

`A=22\cdot20=440`

Notice that the total length of the picture and frame is l=22+x+x=22+2x, while the total width is w=20+x+x=20+2x.

Substitute these dimensions into the area formula:

`\begin{gathered} A=(22+2x)\cdot(20+2x) \\ A=4x^2+40x+44x+440 \\ \Rightarrow A=4x^2+84x+440 \end{gathered}`

Subtract the areas to find the area of the entire frame:

`\text{ Area of frame}=4x^2+84x+440-440=4x^2+84x+0`

The area of the entire frame is 4x²+84x+0.

First-term is 4x², the second term is 84x, and the third term is 0.

To find the area when x=2, substitute x=2 into the expression for the area:

`4(2)^2+84(2)+0=4(4)+168+0=16+168=184`

The area of the frame when x=2 inches is 184 inches squared.

The perimeter is the sum of the side lengths of the frame given as:

`P=2(l+w)`

Substitute l=22+2x and w=20+2x into the formula:

`P=2(22+2x+20+2x)=2(4x+42)=8x+84`

Substitute x=10 to find the perimeter when x=10:

`P=8(10)+84=80+84=164`

The perimeter is 164 inches.

Answers:

The area of the entire frame is 4x²+84x+0.

First-term is 4x², the second term is 84x, and the third term is 0.

The area of the frame when x=2 inches is 184 inches squared.

The perimeter when x=10 is 164 inches.