Question

The diagonals of a rhombus are 14 and 48cm. Find the length of a side of the rhombus.

Answer 1

Explanation:

Let ABCD be a rhombus. So, AC (AC = 14 cm) and BD (BD=48 cm) will be its diagonals. Let us assume that diagonals are intersecting at point O.

Since, diagonals of a rhombus are perpendicular bisector.

`\because \: OA = (1)/(2) * AC \\ \\ </p><p> \therefore \: OA = (1)/(2) * 14</p><p> \\ \\ \huge \red{ \boxed{\therefore \: OA = 7 \: cm}} \\ \\ \because \: OB = (1)/(2) * BD \\ \\ \therefore \: OB = (1)/(2) * 48 \\ \\ \huge \red{ \boxed{\therefore \: OB = 24 \: cm}} \\ \\ In \: \triangle OAB, \: \: \angle AOB=90° \\ \therefore \: by \: Pythagoras \: Theorem \\ AB= √(OA^2 +OB^2 ) \\ = √(7^2 +24^2 ) \\ = √(49+576 ) \\ = √(625 ) \\ \huge \orange{ \boxed{\ \therefore \:AB= 25 \: cm.}}`

Hence, length of a side (or all) is 25 cm.