Question

in a rhombus one diogonal is 7 more than the other & the area of rhombus is 15cm² then find the length of both the diogonal​

Answer 1

Let the other diagonal ( d1 ) be 'x' cm

One of the diagonal ( d2 ) = 7 cm more than the other = (x + 7)

Area of the rhombus = 15 cm²

Also, Area of the diagonal = d1 * d2 / 2 sq.units

⇒ d1 * d2 / 2 = 15

⇒ x(x + 7) / 2 = 15

⇒ x² + 7x = 15 * 2

⇒ x² + 7x = 30

⇒ x² + 7x - 30 = 0

⇒ x² + 10x - 3x - 30 = 0

⇒ x(x + 10) - 3(x + 10) = 0

⇒ (x - 3)(x + 10) = 0

⇒ x - 3 = 0 or x + 10 = 0

⇒ x = 3 or x = - 10

Length of diagonals cannot be negative

⇒ x = 3

Another diagonal ( d1 ) = x = 3 cm

One of the diagonal ( d2 ) = x + 7 = 3 + 7 = 10 cm

Therefore the lengths of the diagonals are 3 cm and 10 cm.

Verification :-

Area of rhombus = d1 * d2 /2 = 3 * 10/2 = 30/2 = 15 cm².

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