A picture 16" x 24" has a frame 1" wide.Approximately how many times greater than the area of the frame is the area of the picture?
a. 5
b. 45
c. 48
d. 80
e. 84
please answer and explain
area of picture = 16(24) = 384 in^2
area of picture and frame = 18(26) = 468
area of frame = 468-384 = 84
picture/frame = 384/84 = appr 4.57
I guess they rounded that off to 5 times.
why 18x26 frame 1"
is not 17 x 25 ?
To find the area of the frame and the picture, we need to calculate the area of the overall dimensions and subtract the area of the inner dimensions.
The dimensions of the picture are given as 16" x 24". Since the frame surrounds the picture on all sides, we need to add twice the width of the frame to each dimension.
The width of the frame is given as 1", so we add 2 times 1" to each dimension:
Width of overall dimensions = 16" + 2(1") = 16" + 2" = 18"
Height of overall dimensions = 24" + 2(1") = 24" + 2" = 26"
Now we can calculate the area of the frame by multiplying the overall dimensions:
Area of the frame = Width of overall dimensions x Height of overall dimensions
Area of the frame = 18" x 26" = 468 square inches
Next, let's calculate the area of the picture by multiplying its dimensions:
Area of the picture = Width of the picture x Height of the picture
Area of the picture = 16" x 24" = 384 square inches
To find how many times greater the area of the picture is compared to the area of the frame, we divide the area of the picture by the area of the frame:
Area of the picture / Area of the frame = 384 square inches / 468 square inches
Calculating this ratio gives us approximately 0.8205.
Therefore, the area of the picture is approximately 0.8205 times the area of the frame.
To find the answer choice that represents this ratio, we need to find the option that is closest to 0.8205.
Looking at the given answer choices:
a. 5
b. 45
c. 48
d. 80
e. 84
None of the answer choices represent a value close to 0.8205. Hence, none of the given answer choices are correct.