Question

The length of each side of a rhombus whose diagonalsare of 10 cm and 24 cm is (a)25 cm (b) 13 cm (c)26 cm (d) 34 cm​

Answer 1

Step-by-step explanation:

We know, diagonals of rhombus are perpendicular bisectors of each other.

Therefore , let the rhombus be ABCD, And Diagonal AC bisects Diagonal BD at E

Diagonal AC = 10 cm

Diagonal BD = 24 cm

seg AE = 1/2 × ( 10 ) = 5 cm

seg BE = 1/2 × ( 24 ) = 12 cm

In triangle AEB

Angle AEB = 90°.... ( diagonals of rhombus are perpendicular bisectors )

Triangle AEB is right angle triangle

by Pythagoras theorem

{ ( 5 ) ^ 2 } + { ( 12 ) ^ 2 } = ( AB )^2

25 + 144 = ( AB )^2

169 = ( AB ) ^2

AB = 13 ....( Taking square root of both sides )

AB = BC = CD = AD.....( sides of rhombus are congruent )

but AB = 13

Therefore each side of rhombus is 13 cm