contestada

a rectangular picture is 6 centimeters longer than it is wide. A frame 1 cm wide is placed around the picture. Write a polynomial that represents the area of the frame.

Respuesta :

Let the width of rectangular frame is x cm. It is given that the frame is 6 cm longer than it is wide. Therefore, the length of the frame will be (x + 6) cm.

A frame of 1 cm is placed all around the picture. This will increase the length and width of the frame from all four sides by 1 cm.

So, the new width will be (x + 2) cm and the new length will be (x +8) cm.

Area of rectangle = Length x Width

So, area of rectangular frame will be (x+2)(x+8) square centimeters.

Simplifying the expression we get:

Area = [tex] x^{2} +2x+8x+16[/tex]

Area = [tex] x^{2} +10x+16[/tex]

The above polynomial represents the Area of the frame.
raphealnwobi

The area of the rectangular frame is (4w + 18) cm²

Area

Area is the amount of space occupied by a two dimensional figure or object.

Let w represent the width of the picture, hence length = w + 6

Area of picture = w(w + 6) = w² + 6w

If a frame of 1 cm is used,:

Length of picture and frame = w + 6 + 2(1) = w + 8, Width of picture and frame = w + 2(1) = w + 2

Area of picture and frame = (w + 8)(w + 2) = w² + 10w + 18

Area of frame = w² + 10w + 18 - (w² + 6w) = 4w + 18

The area of the rectangular frame is (4w + 18) cm²

Find out more on Area at: https://brainly.com/question/25292087

Otras preguntas