Question

ABCD is a square. Find the value of x and the sum of the lengths of diagonals of the square ABCD.

• A. 1 cm and 20 cm
• B. 2 cm and 20 cm
• C. 5 cm and 40 cm
• D. 4 cm and 30 cm

Answer 1

The correct option is A 1 cm and 20 cm


Given, ABCD is a square such that AO = 5 cm and OC = (4x + 1) cm.

In a square, we know that diagonals are equal and they bisect each other.

Hence, AC = BD and AO = OC

$\therefore$ AO = OC = 5 cm
$\Rightarrow$ 4x + 1 = 5 cm
$\Rightarrow$ 4x = 5 cm - 1 cm
$\Rightarrow$ 4x = 4 cm
$\Rightarrow$ x = 1 cm

And
AC = AO + OC
$\Rightarrow$ AC = 5 cm + 5 cm
$\Rightarrow$ AC = 10 cm

Since AC = BD [As diagonals of a square are equal]
$\Rightarrow$ BD = 10 cm

So, sum of diagonals = AC + BD
= 10 cm + 10 cm
= 20 cm

So, the value of x is 1 cm and the sum of lengths of diagonals is 20 cm.