The area of a rhombus is 31 feet squared one diagonal is 14 ft long. Find the length of the other diagonal
The diagonals bisect each other, and are perpendicular. So, drawing the diagonal of 14, you have two triangles with base 14 and altitude 1/2 of the other diagonal. So, if the other diagonal has length 2x, then
2( 1/2 * 14 * x) = 31
x = 31/14
and the other diagonal is 31/7 ft
To find the length of the other diagonal of a rhombus, we can use the formula for the area of a rhombus, which is given by:
Area = (diagonal1 * diagonal2) / 2
Given that the area of the rhombus is 31 ft² and the length of one of the diagonals is 14 ft, we can substitute these values into the formula and solve for the length of the other diagonal:
31 = (14 * diagonal2) / 2
Multiplying both sides of the equation by 2:
62 = 14 * diagonal2
Dividing both sides of the equation by 14:
diagonal2 = 62 / 14
Simplifying:
diagonal2 = 4.43 ft (rounded to two decimal places)
Therefore, the length of the other diagonal is approximately 4.43 ft.
To find the length of the other diagonal of a rhombus given the area and the length of one diagonal, you can use the formula:
Area = (d1 * d2) / 2
Where "Area" is the area of the rhombus, "d1" is the length of one diagonal, and "d2" is the length of the other diagonal.
In this case, we are given that the area is 31 ft^2 and one diagonal is 14 ft long.
Let's substitute the given values into the formula:
31 = (14 * d2) / 2
To solve for "d2", we can multiply both sides of the equation by 2:
62 = 14 * d2
Now, divide both sides of the equation by 14:
d2 = 62 / 14
Simplifying the right side:
d2 = 4.42 ft
Therefore, the length of the other diagonal is approximately 4.42 ft.