Answer:
The lengths of the diagonals are;
15.49 cm and 5.66 cm
Explanation:
The given area of the parallelogram = 30 cm²
Also the length of 2 adjacent sides are 6 cm and 10 cm
Given that the formula for the area of a parallelogram = Base × Height, h where the base is either of the sides of the parallelogram we have;
When the base b = 10 m and the other side, a = 6 cm the diagonal, d is given by the relationship, d² = (a + √(b² - h²))² + h²
10 × h₁ = 30
h₁ = 30/10 = 3
d₁² = (b + √(a² - h₁²))² + h₁² = (10 + √(6² - 3²))² + 3² = 239.92 cm²
d₁ = √(239.92 cm²) = 15.49 cm
The other diagonal can be found from the following relationship;
d₂² = (b - √(a² - h₁²))² + h₁²
d₂² = (10 - √(6² - 3²))² + 3² = 32.08 cm²
d₂ = √(32.08 cm²) = 5.66 cm.