Area of parallelogram is 30cm^2 . If the length of two adjacent
sides are 6 cm and 10cm
respectively. Find its diagonal

The lengths of the diagonals are;

15.49 cm and 5.66 cm

Step-by-step 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.