Question

the length of one side of a rhombus is 61 cm and its area is 1320 sq.cm. find the sum of lengths of the diagonal

Answer 1

AREA OF RHOMBUS= 1/2×D1 × D2
THEREFORE
D1×D2=2640.....(1)
ALSO
(D1/2)^2+ (D2/2)^2=61^2
D1+D2=4 × 61 × 61....(2)
FROM 2 WE GET
D1=14884-D2....(3)
SUBSTITUTING 3 IN 1
(14884-D2)D2=2640
14884D2-D2^2=2640
FACTORISING THE Q.E WE GET

Answer 2

Length of one side of Rhombus = 61 cm

→As, all sides of rhombus are equal, so all sides of rhombus will be of length 61 cm.

Area of Rhombus = $\frac{1}{2}\times{\Text {Product of Diagonals}}$

          →   1320 cm²  = $\frac{1}{2}\times D_{1}\times D_{2}$

→ $D_{1}\times D_{2}= 1320 \times 2= 2640$

As Diagonals of rhombus Bisect each other at Right angles.

→  $[\frac{D_{1}}{2}]^2+[\frac{D_{2}}{2}]^2=(61)^{2}$

→$[{D_{1}]^{2} +[{D_{2}]^{2} = 4 \times 3721$

                                               =      14,884 cm²

→$[D_{1} + D_{2}]^{2}= [{D_{1}]^{2} +[{D_{2}]^{2}+2D_{1} \times D_{2}$

→$[D_{1} + D_{2}]^{2}$= 14,884 + 2,640

                                               = 17,524 cm²

→ D_{1} + D_{2} = $\sqrt{17,524}$ = 132.4 cm