Question

a student sketched some art on an 8 inch x 10 inch piece if paper he wants to resize it to fit an 4 inch x 6 inch frame. What percent of the original sketch was still able to be included?

Answer 1

The student can include 30% of the original 8 inch by 10 inch sketch into the 4 inch by 6 inch frame by calculating the area of both and finding the percentage of the area that overlaps.

Step-by-step explanation:

The student originally had an 8 inch by 10 inch piece of paper which he wanted to resize to fit a 4 inch by 6 inch frame. To determine what percent of the original sketch can be included in the new frame size, we must first calculate the area of both the original sketch and the resized sketch. The area of the original sketch is 8 inches × 10 inches = 80 square inches. The area of the new frame size is 4 inches × 6 inches = 24 square inches.

Next, we find the ratio of the new frame size to the original sketch size to determine the scale factor. Finally, to find the percentage of the original sketch that will fit in the new frame, we divide the area of the new frame by the area of the original sketch and multiply by 100 to convert to a percentage: (24 square inches / 80 square inches) × 100 = 30%.

Therefore, 30% of the original sketch was able to be included in the new frame size.

Answer 2

The picture is originally 11 inches wide by 8.5
inches tall. It gets scaled down to a new width of 7 inches. We need to find the new height. To do this, we write a proportion:

8.5/11=x/7

Cross multiply:
11x = 59.5

Divide:
X = 5.41

The size of the picture is 5.41" x7", but the size of the frame is 5" x7". The part of the picture's area that is included in the frame is:
(5 × 7) / (5.41 × 7)
= 5/ 5.41
= 0.924

92.4% of the picture is inside the frame.