A rhombus shaped filed has green grass for 12 cows to graze. If each side of the rhombus is 30 m and its diagonal is 48 m, then the area of the grass field which each cow can graze is
Question
A rhombus shaped filed has green grass for 12 cows to graze. If each side of the rhombus is 30 m and its diagonal is 48 m, then the area of the grass field which each cow can graze is
Solution
To find the area each cow can graze, we first need to find the total area of the rhombus-shaped field.
The formula for the area of a rhombus is 1/2 * (product of the diagonals). In this case, we only have one diagonal, so we need to find the other.
We can use the Pythagorean theorem to find the other diagonal. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In a rhombus, the diagonals are perpendicular bisectors, meaning they intersect at a right angle and divide each other into two equal parts. So, we can form a right triangle with half of one diagonal and one side of the rhombus.
Using the Pythagorean theorem, (30^2) = (48/2)^2 + b^2, where b is half of the other diagonal. Solving for b, we get b = sqrt[(30^2) - (48/2)^2] = 24 m. So, the other diagonal is 2b = 48 m.
Now, we can find the area of the rhombus: 1/2 * (48 m * 48 m) = 1152 m^2.
Finally, to find the area each cow can graze, we divide the total area by the number of cows: 1152 m^2 / 12 cows = 96 m^2/cow.
So, each cow can graze an area of 96 m^2.
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