The lenth of one of the diagonals of a rhombus is greater than other by 5cm.if its area is 18 sqcm Find lenght of the diagonals of rhombus Solve with Word problem step
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Let length one diagonal be x.
The length of other diagonal is x + 5
Given area of rhombus = 18 sq cm.
Area of rhombus = d₁ * d₂/2 where d₁ and d₂ are diagonals.
=> x * x + 5 /2 = 18
=> x² + 5x = 36
=> x² + 5x - 36 = 0
=> x² + 9x - 4x - 36 = 0
=> x(x + 9) - 4(x +9) = 0
=> (x + 9 ) (x - 4) = 0
=> x + 9 = 0 or x - 4 = 0
=> x = -9 or 4.
Since x cannot be negative, the x = 4 cm.
Thus length of one diagonal = 4 cm.
Length of second diagonal = 4 + 5 = 9 cm.
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