Question

In the trapezium ABCD, AB || DC, AB = 9 cm, DC = 6 cm and BD = 12 cm. The
diagonals AC and BD intersect at O. Find the length of BO

Answer 1

Given:-

• AB||CD.
• AB = 9cm
• DC = 6cm
• BD = 12cm
• Diagonals AC and BD intersect at O.

To Find:-

• Length of BO =?

Solution:-

In ∆COD and ∆AOB,

$\sf{\angleDOC}$=$\sf{\angleAOB}$ {Vertically opposite}

$\sf{\angleDOC}$=$\sf{\angleAOB}$ {Alternate Angles}

$\sf\implies{\angleCOD}$=∆AOB {AA similarly}

Let OB = xx cm

$\sf\dfrac{AB}{CD}$=$\sf\dfrac{OB}{OD}$

$\sf \frac{9}{6} = \frac{x}{12 - x} \\ \\ \sf 108 - 9x = 6x \\ \\ \sf 15x = 108 \\ \\ \sf x = 7.2cm$

Hence,Length of BO = 7.2cm