Asked by Anonymous
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.
perimeter is 100 cm, find the length of the sides and the diagonals.
Answers
Answered by
mathhelper
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
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