The area of a kite is 78 in. squared. The length of one diagonal is 12 in. What is the length of the other diagonal?
Show work.
The formula for the area of a kite is:
A = (d1 x d2)/2
where d1 and d2 are the lengths of the two diagonals. We are given that the area is 78 in. squared and one diagonal (d1) is 12 in. Plugging in these values, we can solve for the other diagonal (d2):
78 = (12 x d2)/2
Multiplying both sides by 2 and then dividing by 12, we get:
d2 = 13
Therefore, the length of the other diagonal is 13 in.
To find the length of the other diagonal of the kite, we can use the formula for the area of a kite:
Area = (1/2) × d1 × d2
Where d1 and d2 are the lengths of the diagonals.
Given that the area is 78 in² and one diagonal (d1) is 12 in, we can rearrange the formula to solve for d2:
78 = (1/2) × 12 × d2
To solve for d2, we can multiply both sides of the equation by 2 and divide by 12:
2 × 78 = 12 × d2
156 = 12 × d2
Now, divide both sides of the equation by 12:
156 / 12 = d2
Thus, the length of the other diagonal is:
d2 = 13 in.
Therefore, the length of the other diagonal is 13 inches.
To find the length of the other diagonal, we can use the formula for the area of a kite:
Area of a Kite = 1/2 * (Product of the diagonals)
Given that the area of the kite is 78 square inches and one diagonal is 12 inches, we can substitute these values into the formula:
78 = 1/2 * (12 * Length of the other diagonal)
To find the length of the other diagonal, we can solve for it algebraically:
Multiply both sides of the equation by 2:
2 * 78 = 12 * Length of the other diagonal
156 = 12 * Length of the other diagonal
Divide both sides of the equation by 12:
Length of the other diagonal = 156 / 12
Length of the other diagonal = 13 inches
Therefore, the length of the other diagonal is 13 inches.