Question

ABCD is a rectangle. If OB = $x+2$ and AC = $5x-2$, then find the measure of AC.

• A. 7 units
• B. 8 units
• C. 6 units
• D. 9 units

Answer 1

The correct option is B 8 units

BD = BO + OD ...(i)
AC = AO + OC ...(ii)
Since, diagonals are equal and bisect each other.
BD = AC
So, AC = BO + OD ...(iii)

Also, OD = OB ...(iv)
(Substitute (iv) in (iii))

AC = OB + OB = 2OB
So, $5x-2=2x+2$
$\Rightarrow$ $5x-2=2x+4$
$\Rightarrow$ $5x-2x=4+2$
$\Rightarrow$ $3x=6$
$\Rightarrow$​ $x=2$

AC = $5x-2=(5\times 2)-2$
= $10-2$
= $8$ units