Question

Please help me how do I solve and draw the problem ?

Answer 1

Side of the rhombus is 12 cm. Let d1 = 2x cm , so d2 = 2x+6 cm

Now, 12^2 = x^2 + (x+3)^2 = 2x^2 + 6x+9 = 144, or

2x^2 + 6x-135=0, or

x^2+3x-67.5 = 0

x1 = [-3 +(9+270)^0.5]/2

= [-3+279^0.5]/2

= [-3+16.70329309]/2 = 6.851646544 cm [x2 will be negative and so inadmissible]

So d1 = 2x6.851646544 = 13.70329309 cm and d2 = 19.70329309 cm.

So the area of the rhombus is 13.70329309x19.70329309/2 = 135 sq cm.