Diagonal of rhombus meet at centre and form right angle triangle. Length of base is 10 cm and height is 24 cm. Find hypotenuse and perimeter of rhombus.

Explanation

solution:
diagonals meet at the centre and forms right-angled triangles.
so by using pythagoras theorem
length of the base = `10/2 = 5cm`
length of the height = `24/2 = 12cm`
`hypotenuse^2 = side^2+ side^2`
`h^2 = 5^2+ 12^2`
`h^2 = 25 + 144`
`h^2 = 169`
on taking square root
we get,
hypotenuse = `13`
since `13xx13 = 169`
and `sqrt 169 = 13`
hence the side of the rhombus is `13cm`.
perimeter of the rhombus = `4xxside`
perimeter of the rhombus = `4xx13`
perimeter of the rhombus = `52cm`
therefore, the perimeter of the rhombus is `52cm`.