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

Question

2 years ago

10

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!!

2 answers:

gogolik [260] · Answer 1 · 2022-02-10T08:42:06+03:00

6 0

13 i think i hope so

WARRIOR [948] · Answer 2 · 2022-02-10T10:41:56+03:00

Answer:

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

Step-by-step explanation:

Givens

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.