If length of each side of a rhombus ABCD is 16 cm and ang ABC 120o then what is the length in cm of ...........

Quantitative Aptitude (CPO) Geometry

If length of each side of a rhombus ABCD is 16 cm and ∠ABC = 120^o, then what is the length (in cm) of BD?

14√3

Let’s break it down step-by-step:

- In any rhombus, all sides are equal. Here, each side = 16 cm.

- For rhombus ABCD, ?ABC = 120°.

- To find BD, draw diagonal BD. In any rhombus, diagonals bisect each other at right angles.

- Triangle BCD has sides BC = CD = 16 cm and angle ?BCD = 120°. BD is opposite this angle.

- Use the cosine rule: BD² = 16² + 16² - 2×16×16×cos(120°).

- cos(120°) = -1/2. Plug in:

BD² = 256 + 256 - 2×16×16×(-1/2)

= 512 + 256 = 768

BD = v768 = 16v3 cm

Now, let’s look at the options:

- (1) 24: Doesn’t fit the math

- (2) 12: Too small

- (3) 16: Just the side, not BD

- (4) 16v3: Matches perfectly with the calculation

Option:4, 16v3 is correct.

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