SOLUTION: city park is a right triangle with a base of 40 yards and a height of 25 yards. On a map, the park has a base of 40 inch and a height of 25 inch. What is the ratio of the area of t

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Question 1027813: city park is a right triangle with a base of 40 yards and a height of 25 yards. On a map, the park has a base of 40 inch and a height of 25 inch. What is the ratio of the area of the triangle in the map to the area of City Park?
Found 2 solutions by Cromlix, Theo:
Answer by Cromlix(4381) (Show Source):
You can put this solution on YOUR website!
Hi there,
Convert yards into inches
Base = 40 yards = 1440 inches
Height = 25 yards = 900 inches
Base (Map)/Base (Actual)
40/1440 = 1 : 36
Height (Map)/Height (Actual)
25/900 = 1 : 36
Hope this helps :-)

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the scale of the height and the width is 1 inch equals 1 yard.

the scale of the area would be 1 square inch equals 1 square yard.

for example:

the area of a triangle is equal to 1/2 * base * height.

the base on the map is 40 inches and the height on the map is 25 inches.

the area on the map is therefore 1/2 * 40 * 25 = 500 square inches.

the base in the real world is 40 yards and the height in the real world is 25 yards.

the area in the real world is therefore equal to 1/2 * 40 * 25 = 500 square yards.

the ratio of the area on the map to the area in the real world is 500 square inches / 500 square yards equals 1 square inch / 1 square yard.

that's 1 square inch to 1 square yard.

in general, if the scale in the linear measurements were a/b, then the scale in area would be (a/b)^2.

since your scale in linear measurements is 1/1, then the scale in area would be (1/1)^2 which is equal to 1/1.

assuming the scale in linear measurements were 1/2, then the scale in area would be (1/2)^2 = 1^2/2^2 = 1/4.