Question

ABCD is a rectangle. If OB = x + 2 and AC = 5x - 2, then find the measure of AC. (3 marks)

Answer 1

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) (1 mark)
(Substitute (iv) in (iii))

AC = OB + OB = 2OB
So, 5x - 2 = 2 (x + 2)
$\Rightarrow$ 5x - 2 = 2x + 4
$\Rightarrow$ 5x - 2x = 4 + 2
$\Rightarrow$ 3x = 6
$\Rightarrow$​ x = 2 (1 mark)

AC = 5x - 2 = (5 $\times$ 2) - 2
= 10 - 2
= 8 units (1 mark)