Question

The diagonals of a rhombus are in the ratio 5:12. If its perimeter is 104 cm, find the lengths of the sides and the diagonals.​

Answer 1

A rhombus has four sides equal in length

Hence

a=1044=26 cm

For the ratio part, let x be the common factor

so we have

one diagonal 5x and the other 12x .

So we have

Half diagonals are 2.5x and 6x .

Hence using the right-angle WOZ we have

(2.5x)2+(6x)2=262

x=4 cm

Hence the diagonals are

20 cm and 48 cm.....