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11. Keng creates a painting on a rectangular canvas with a width that is four inches longer
than the height, as shown in the diagram below.

L= h +4 and H = h


A. Write a polynomial expression, in simplified form, that represents the area of the
canvas.

Keng adds a 3-inch-wide frame around all sides of his canvas.

B. Write a polynomial expression, in simplified form, that represents the total area of the canvas and the frame.

11 Keng creates a painting on a rectangular canvas with a width that is four inches longer than the height as shown in the diagram below L h 4 and H h A Write a class=

Respuesta :

Part A

Answer:  h^2 + 4h

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Explanation:

We multiply the length and height to get the area

area = (length)*(height)

area = (h+4)*(h)

area = h(h+4)

area = h^2 + 4h .... apply the distributive property

The units for the area are in square inches.

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Part B

Answer:  h^2 + 16h + 60

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Explanation:

If we add a 3 inch frame along the border, then we're adding two copies of 3 inches along the bottom side. The h+4 along the bottom updates to h+4+3+3 = h+10 along the bottom.

Similarly, along the vertical side we'd have the h go to h+3+3 = h+6

The old rectangle that was h by h+4 is now h+6 by h+10

Multiply these expressions to find the area

area = length*width

area = (h+6)(h+10)

area = x(h+10) ..... replace h+6 with x

area = xh + 10x .... distribute

area = h( x ) + 10( x )

area = h( h+6 ) + 10( h+6 ) .... plug in x = h+6

area = h^2+6h + 10h+60 .... distribute again twice more

area = h^2 + 16h + 60

You can also use the box method or the FOIL rule as alternative routes to find the area.

The units for the area are in square inches.