A photograph is 20cm long and 15cm wide. The length of a small print of the photograph is 4cm
Find:
A. The width of the small print
B. The ratio of the areas of the two photographs
A. 15 / 20 = w / 4
B. the ratio of the areas is the square of the ratio of the side lengths
... area ratio = (20 / 4)^2
To find the width of the small print, we can set up a proportion comparing the length and width of the two photographs.
Let's let x represent the width of the small print.
Using the given information:
Length of the original photograph = 20 cm
Width of the original photograph = 15 cm
Length of the small print = 4 cm
We can set up the proportion:
20 cm / 15 cm = 4 cm / x
Cross-multiplying:
20 cm * x = 15 cm * 4 cm
Simplifying:
20x = 60 cm^2
Dividing both sides by 20:
x = 3 cm
Therefore, the width of the small print is 3 cm.
To find the ratio of the areas of the two photographs, we first need to calculate the area of each photograph.
Area of the original photograph = length * width = 20 cm * 15 cm = 300 cm^2
Area of the small print = length * width = 4 cm * 3 cm = 12 cm^2
The ratio of the areas is:
300 cm^2 : 12 cm^2
Simplifying:
25 : 1
Therefore, the ratio of the areas of the two photographs is 25 : 1.
To find the width of the small print, we can set up a proportion using the given information.
Let's define:
L1 = Length of the original photograph = 20cm
W1 = Width of the original photograph = 15cm
L2 = Length of the small print = 4cm
W2 = Width of the small print (unknown)
We can set up the proportion:
L1/W1 = L2/W2
Substituting the given values:
20/15 = 4/W2
To solve for W2, we can cross-multiply and solve for W2:
20W2 = 4 * 15
20W2 = 60
W2 = 60/20
W2 = 3
Therefore, the width of the small print is 3 cm.
Now let's move on to finding the ratio of the areas of the two photographs.
The area of the original photograph can be calculated by multiplying its length (20 cm) by its width (15 cm):
Area1 = L1 * W1 = 20 cm * 15 cm = 300 cm^2
Similarly, the area of the small print can be calculated by multiplying its length (4 cm) by its width (3 cm):
Area2 = L2 * W2 = 4 cm * 3 cm = 12 cm^2
The ratio of the areas is calculated by dividing the larger area by the smaller area:
Ratio = Area1 / Area2 = 300 cm^2 / 12 cm^2 = 25
Therefore, the ratio of the areas of the two photographs is 25.