Question

A 5 inch × 7 inch photograph is placed inside a picture frame. Both the length and width of the frame are 2x inches larger than the width and length of the photograph. Which expression represents the perimeter of the frame?

Answer 1

Answer:

Now lets see… you want the expression for calculating the perimeter of the frame only.

Step-by-step explanation:

So now as we know that the length and width of the photograph are given, which means that the photograph is a rectangle shaped.

Now the formula for calculating the perimeter of the rectangle is given by:-

Perimeter (rect.) = 2 (Length + width).

Here we have Length of the picture = 7 inch. And width = 5 inch.

Next we are told that the picture is to be placed in the rectangular frame that is 2x inches larger than picture length and width,

So we have

Length of the frame = 2x + 7inch.

Width of the frame = 2x + 5 inch.

Now the expression for calculating the perimeter by same formula we get,

Perimeter of the frame = 2 (2x + 7 + 2x +5) = 2 (4x + 12).

(now the above calculation has been done considering 2x = 2 of x and not 2 times.)

Answer 2

Perimeter of the frame is 8x + 24

Solution:

Length of photograph is 7 inch whereas the width of photograph is 5 inch placed in a frame of twice the length and width of the photograph.

Let us take length and breadth of the photo frame as 2x.

Therefore, length given for the frame is (2x+5) inches and width is (2x+7) inches.

Hence, perimeter of the frame is 2( length + breadth) = 2 ((2x+5) + (2x+7)) = 8x + 24.