Maths · Relations between roots and coefficients, nature of roots
The area of a rhombus is 2016 sq and its side is The lengths of the diagonals (i
The area of a rhombus is 2016 sq \( \mathrm{cm} \) and its side is \( 65 \mathrm{cm} . \) The lengths of the diagonals (in cm) respectively are
- A. 125,35
- B. 126,32
- C. 132,26
- D. 135,25
Step-by-step solution
Area of rhombus = (1/2) * d1 * d2 = 2016 => d1*d2 = 4032. Side^2 = (d1/2)^2 + (d2/2)^2 = 4225 => d1^2 + d2^2 = 16900. Let d1 and d2 be roots of t^2 - (d1+d2)t + d1*d2 = 0. Compute (d1+d2)^2 = d1^2+d2^2+2d1*d2 = 16900+8064=24964 => d1+d2=158. Then d1,d2 are roots of t^2 - 158t + 4032 = 0 => (t-126)(t-32)=0 => d1=126, d2=32.