10. A square picture has a 1-inch frame around it. If the

Mathematics

1 answer:

dezoksy [38]3 years ago

6 0

Answer:

361 sq, inches.

Step-by-step explanation:

Let us assume that the dimensions of the square picture are P in × P in.

So, the area of the picture alone is, A = P²

Now, if the photo has a frame of 1 inch wide, then the dimensions of the photo with frame are (P + 2) in × (P + 2) in.

So, the area of the photo with frame is A' = (P + 2)(P + 2) = (P + 2)²

Now, the area of the frame alone is 80 sq. inches.

Hence, A' - A = 80

⇒ (P + 2)² - P² = 80

⇒ 4P + 4 = 80

⇒ 4P = 76

⇒ P = 19 inches.

So, the area of the picture is = 19² = 361 sq. inches. (Answer)

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