Question

In the rectangle ABCD given below if OA = (x + 3) cm, OC = 18 cm,
then find the values of:
(i) x
(ii) length of diagonal BD.

Answer 1

I think the answer should be first one x

Answer 2

Given:

In the rectangle ABCD given below if OA = (x+3) cm, OC = 18 cm.

To find:

• Value of x

• Value of diagonal BD

Calculation:

As per properties of a rectangle , we can say that:

• Both the diagonals are equal in length (i.e. BD = AC).

• Diagonals bisect each other.

Since, diagonals bisect each other, we can say that diagonal AC is bisected by diagonal BD such that:

$\therefore \: OA = OC$

$\implies \: x + 3 = 18$

$\implies \: x = 18 - 3$

$\implies \: x = 15 \: cm$

So, value of x = 15 cm.

Now , since both diagonals are equal in length, we can say that:

$\therefore \: AC = BD$

$\implies \:OA + OC = BD$

$\implies \:OA + OA = BD$

$\implies \:BD = 2(OA)$

$\implies \:BD = 2(x + 3)$

$\implies \:BD = 2(15 + 3)$

$\implies \:BD = 2 \times 18$

$\implies \:BD = 36 \: cm$

So, diagonal BD length is 36 cm.

Hope It Helps.