The perimeter and the length of one of the diagonals of a rhombus is 26 cm and 5 cm respectively. Find the length of its other diagonal (in cm).

Given : ABCD is a rhombus and perimeter(ABCD) = 26 cm and BD = 5 cm

To find : AC = ?

Solution : Diagonals of a rhombus bisect each other at right angle.

=> BE = $$\frac{5}{2}=2.5$$ cm and side of rhombus = AB = $$\frac{26}{4}=6.5$$ cm

Thus, in right $$\triangle$$ AEB,

=> $$(AE)^2=(AB)^2-(BE)^2$$

=> $$(AE)^2=(6.5)^2-(2.5)^2$$

=> $$(AE)^2=42.25-6.25=36$$

=> $$AE=\sqrt{36}=6$$ cm

$$\therefore$$ AC = $$2\times6=12$$ cm

=> Ans - (B)