Question

In rhombus ABCD, OA + OB = 14 and 2(OC) + 3(OD) = 36. Which is BD?


Answer 12
14
15
16

Answer 1

16 because then OB=8 OA=6 OC=6 and OD=8 so wen you plug those in 2*6+3*8 =36 and 6+8=14

Answer 2

BD = 16

Diagonals of a rhombus bisect each other
so OA = OC AND OB = OD --------(A)

We r given OA + OB = 14 ------------(1)
and 2(OC) + 3(OD) = 36 ------------(2)

Using (A), (2) can be written as
2OA + 3OB = 36 ---------------(3)

Treating (1) and (3) as pair of simultaneous linear equations, we can solve as follows:

Multiplying (1) by -2 and adding (3) to it we get
-2OA - 2OB = -28
2OA + 3OB = 36

OB = 8
OD = OB = 8
and BD = OB + OD = 8 + 8 = 16