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sp2606 [1]
3 years ago
5

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?

Mathematics
2 answers:
rewona [7]3 years ago
7 0

The lengths of the top/bottom interior edges are $5-2=3$ inches (since there is 1 inch of frame to either side of the interior rectangular hole). Let the lengths of the left/right interior edges be $x$ inches. Then, the lengths of the left/right exterior edges are $x+2$ inches. The area of the frame is equal to the area of the frame rectangle minus the area of the hole. This is equal to $5\cdot(x+2)-3x=2x+10$. Since we are given that this area is 18 square inches, we have the equation $2x+10=18\Rightarrow x=4$. So the dimensions of the interior hole are $3\times4$. Thus, the sum of the four interior edges is $3+4+3+4=\boxed{14}$ inches.

Leni [432]3 years ago
6 0

Answer:

46

Step-by-step explanation:

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