A picture frame, 5 cm wide, has a length which is twice the width, x cm. a) Find an expression for the total area of the frame and picture. b) Find an expression in expanded form for the area of...

A picture frame, 5 cm wide, has a length which is twice the width, x cm.

a) Find an expression for the total area of the frame and picture.

b) Find an expression in expanded form for the area of picture only.

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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We know that the breadth (width) of the outside edge of the picture (ie including the frame) = x cm.

`therefore b=x `

As the length is twice the outside breadth (width), we know that `l=2 times b`

`therefore l=2x`

And we know that the area of a rectangle is  `l times b`

`therefore A=2x times x`

`therefore = 2x^2`

For the picture only, we know that the frame is 5cm in width and we must deduct 5 cm from each side to find the length and breadth (width) of the picture itself (without the frame). 

`therefore l= 2x-10 and b=x-10`

`therefore A=(2x-10)(x-10)`

`= 2x^2-20x-10x+100`

`= 2x^2-30x +100`

Ans:

The total area of the outside edge of the picture and frame is `2x^2`

and the expression representing the area of the picture only is `2x^2-30x+100`

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