Question

A rectangular picture frame is made from one-inch-wide pieces of wood. The area of just the frame is 18 square inches, and one of the outer edges of the frame is 5 inches long. What is the sum of the lengths of the four interior edges of the frame?

HELP!!!

Please!!

Answer 1

13 i think i hope so

Answer 2

All four interior edges are 4 inches, 3 inches, 4 inches and 3 inches.

Explanation:

Givens

• The area of the frame is 18 square inches.
• The wide of the frame is 1 inch.
• One of the outer edges of the fram is 5 inches long.

If one side is 5 inches long and the wide is 1 inch, then the inner side is 3 inches long, becase we must subtract the 2 inches of the wide.

The image attached shows all relations we need to make regarding both areas.

The inner area is defined as

`A_(inner)=(b-2)3`

The area of the whole

`A_(whole)=5b`

The area of the frame is defined as the difference of the inner area and the whole area

`A_(frame)=A_(whole)-A_(inner)\\ 18=5b-3(b-2)`

Now, we solve for
`b`

`18=5b-3(b-2)\\18=5b-3b+6\\18-6=2b\\b=(12)/(2)\\ b=6`

The interior each is defined as b-2, so its length is

`b-2=6-2=4`

Therefore, the interior edges are 4 inches and 3 inches long.

All four interior edges are 4 inches, 3 inches, 4 inches and 3 inches.