The lengths of the diagonals of a rhombus are in the ratio 3 : 4. If the
perimeter is 100 cm, find the length of the sides and the diagonals.
The Grouch on Sesame Street once called a rhombus a "squished square", so all the sides are equal
if the perimeter is 100, then 4s = 100 , s = 25
each side is 25 cm.
In a rhombus the diagonals right-bisect each other, creating 4 congruent
right-angled triangles with legs 3x and 4x ,
(note the ratio of half-diagonals will remain as 3 : 4 )
so , by Pythagoras
(3x)^2 + (4x)^2 = 25^2
9x^2 + 16x^2 = 625
25x^2 = 625
x^2 = 25
x = 5
Recall the diagonals were in ratio of 3:4 = 3x : 4x
So the diagonals are 15 cm and 20 cm