The diagonals of a kite are in the ratio 3:2. The area of the kite is 27 cm². Find the length of both diagonals.
Answer (2)
We are given that a kite has diagonals in the ratio of 3 : 2 and an area of 27 cm². To find the length of both diagonals, we can use the area formula of a kite which is Area = (diagonal 1 × diagonal 2) / 2. Let's denote the lengths of diagonals as 3x and 2x, respectively, based on the given ratio.
Substituting into the area formula, we get: 27 = (3x × 2x) / 2 27 = 3x × x 27 = 3x² 9 = x² x = 3 cm.
Now we can find the actual lengths of the diagonals: Diagonal 1 = 3x = 3 × 3 = 9 cm Diagonal 2 = 2x = 2 × 3 = 6 cm
Therefore, the lengths of the diagonals of the kite are 9 cm and 6 cm.
The lengths of the diagonals of the kite are 9 cm and 6 cm. This is derived from the area formula for a kite and the given ratio of the diagonals. By substituting the values into the equation and solving for the variable, we obtained the lengths successfully.
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