Length and width

Question

Last question, I promise. Thanks!

 

A rectangular painting measures 10 inches by 18 inches and contains a frame of uniform width around the four edges. The perimeter of the rectangle formed by the painting and it's frame is 64 inches. Determine the width of the frame. 

 

(I know the question is badly worded. Basically, the picture on the inside is 10 by 18. The frame on the outside has a perimeter of 64. What is the space from the picture to the outside of the frame? I solved it and got the answer of 2 inches, but am not sure I did it right.)

Answer 1

10 + 2x represents the width of the frame

18 + 2x represents the length of the frame

 

10 + 2x + 18 + 2x = 32    (using just one length and one width)

4x + 28 = 32

4x = 4

x = 1

 

Check

Width is 12, length is 20

2(12 + 20)

2(32)

64

Answer 2

Lets's assume the width of the frame is x inch

Thus the perimeter of the frame must be = 2 [(10+2x)+(18+2x)] inches

 

Given that,

2 [(10+2x)+(18+2x)] = 64

=> (10+2x)+(18+2x)=32 , dividing both sides by 2

=> 28+4x=32 , adjusting the operators and coefficients

=>4x=4 , subtracting 28 from both sides

=>x=1, dividing both sides by 4

 

Therefore the frame is 1 inch wide.