Draw a rhombus ABCD. if AC= 6cm and AB=5cm, find the length of BD.

1.	Draw a rhombus ABCD. if AC= 6cm and AB=5cm, find the length of BD.
Answer» (REFER to the attachment) GIVEN:- AC (1st diagonal) = 6 cm AB = 5 cm To Find:- Length of BD ( other diagonal). SOLUTION:- We KNOW that in a rhombus, DIAGONALS bisect each other at right angles. So by applying Pythagoras THEOREM, $\large{\sf {(hypo)}^{2} = {(side)}^{2} + {(base)}^{2} }$ where, hypotenuse = hypo, side = s, base = b. $\large{\sf {(AB)}^{2} = {(AO)}^{2} + {(BO)}^{2}}$ $\large{\sf = > {(25)}^{2} = {(3)}^{2} + {(BO)}^{2}}$ $\large{\sf = > 25 = 9 + {(BO)}^{2} }$ $\large{\sf = > 25 - 9 = {(BO)}^{2}}$ $\large{\sf = > 16 = {(BO)}^{2}}$ Now by square ROOTING both sides, $\large{\sf => \sqrt{16} = BO}$ $\large{\sf =>BO \: = \frac{ + }{ - } 4 \: }$ Length of BO = 4 cm Therefore Length of BD = 2 × 4 = 8 cm. $\large\red\therefore\boxed{\sf{\red{Length\:of\:BD\:=\:8\:cm.}}}$

Answer»

(REFER to the attachment)