Suppose you want to enlarge a 4-inch by 6-inch photograph as much as possible so that it fits on a bulletin board that is 24 inches high. What will the width of the photograph be if the sides must remain in proportion?
a. What is the ratio of the height of the original photograph to the height of the enlargement?
b. What is that ratio in simplest form?
Original photo = 4-1n. by 6-in.
enlarged photo = 16-in by 24-in.
a. Ratio = 6:24.
b. 6:24 = 1:4.
Thanks Henry!
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a. Well, if we want to enlarge the photograph while keeping the sides in proportion, we need to find the ratio of the original height to the enlargement height. The original photograph is 4 inches by 6 inches, and the enlargement needs to be 24 inches high. So the ratio is 6/24 or 4/16.
b. To simplify the ratio, we can divide both the numerator and denominator by their greatest common divisor. In this case, the greatest common divisor of 4 and 16 is 4. So the simplified ratio is 1/4.
Therefore, the width of the photograph will be 1/4 of the height, so it will be 1/4 of 24 inches, which is 6 inches.
To find the width of the photograph that fits on the bulletin board while maintaining the proportional relationship with the height, we need to determine the ratio of the original photograph's height to the enlargement's height.
a. The ratio of the height of the original photograph to the height of the enlargement can be found by dividing the height of the original photograph by the height of the enlargement.
Original photograph height: 4 inches
Enlarged bulletin board height: 24 inches
Ratio = Original photograph height ÷ Enlarged bulletin board height
Ratio = 4 inches ÷ 24 inches
b. To simplify the ratio, we can divide both the numerator and denominator of the ratio by their greatest common divisor (GCD).
The GCD of 4 and 24 is 4.
Simplified ratio = 1 inch ÷ 6 inches
Therefore, the ratio of the height of the original photograph to the height of the enlargement is 1:6.
This means that for every inch of height in the original photograph, the enlargement will have a height of 6 inches.
To determine the width of the photograph for the enlargement, we can use the same ratio and multiply the width of the original photograph by the simplification factor.
Original photograph width: 6 inches
Enlarged photograph width = Original photograph width × Ratio
Enlarged photograph width = 6 inches × 1:6
Enlarged photograph width = 1 inch
Therefore, if the height of the enlargement is 24 inches, the width of the photograph, while maintaining the proportional relationship, will be 1 inch.