7. If the length of one of the diagonals of a rhombus is 7cm more than that of the other diagonal, and its. area is 15cm2 then find the length of the two diagonals
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Solution :-
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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