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madam [21]
3 years ago
10

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 o

f 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!!

Mathematics
2 answers:
gogolik [260]3 years ago
6 0
13 i think i hope so
WARRIOR [948]3 years ago
3 0

Answer:

<h2>All four interior edges are 4 inches, 3 inches, 4 inches and 3 inches.</h2>

Step-by-step 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=\frac{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.

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