Question

in the given figure AC is 1.4 CM more than BD if sum of length of diagonal is 12 CM then find a OB OC and OD​

Answer 1

Given:

please find the attachment.

To Find:

OB, OC, and OD= ?

Solution:

Given:

AC= 1.4+BD

AC+BD = 12

$\to AC= \ 1.4+\ BD ....(i)\\\\\ \to AC\ +\ BD \ = \ 12...(ii)\\\\ \to AC= 12 - BD$

put the AC value in equation (i)

$\to 12 -BD = 1.4 +BD\\\\\to 12 - 1.4 = BD+BD\\\\\to 12 - 1.4 = 2BD\\\\\to 10.6 = 2BD\\\\\to BD= \frac{10.6}{2}\\\\\to BD= 5.3$

Put the BD value in equation (ii)

$\to AC +BD =12\\\\\to AC+ 5.3 =12\\\\\to AC = 6.7$

$\bold{OB = OD = \frac{BD}{2}\ \ \ and \ \ \ OC =\frac{AC}{2}\\\\}$

$\to OB = OD = \frac{5.3}{2}\ \ \ and \ \ \ OC =\frac{6.7}{2}\\\\\to OB = OD = 2.65 \ \ \ and \ \ \ OC = 3.35$

Answer 2

OA = OC = 3.35cm

OB = OD = 2.65cm

Explanation:

Sum of diagonals = 12 cm.

AC is 1.4cm more than BD.

AC - BD = 1.4 --- (1)

AC + BD = 12 --- (2)

Adding 1 and 2, we get:

2 AC = 13.4

So AC = 13.4/2 = 6.7 cm

Substituting AC in 2, we get:

6.7 + BD = 12

BD = 12 - 6.7 = 5.3 cm

OA = OC = AC/2 = 6.7/2 = 3.35cm

OB = OD = BD/2 = 5.3/2 = 2.65cm