the diagonal of a rombus are in the ration 5:12 if its parimeter is 104 cm,find the length of the sides and the digonals
akaka:
please i need it fast
Answers
Answered by
4
The diagonals are 5x , 12x .
By Pythagoras theorem;
(5x/2)²+(12x/2)² = Hypotenuse².
25x²+144x² / 4 = Hypotenuse².
Hypotenuse² =(13x/2)²
Hypotenuse = 13x/2 .
Now, 4(13x/2) = 104
26x = 104
x = 4 .
Therefore, The side of rhombus = 4cm .
Also the diagonals are 5(4) and 12(4) :- 20 , 48 respectively.
By Pythagoras theorem;
(5x/2)²+(12x/2)² = Hypotenuse².
25x²+144x² / 4 = Hypotenuse².
Hypotenuse² =(13x/2)²
Hypotenuse = 13x/2 .
Now, 4(13x/2) = 104
26x = 104
x = 4 .
Therefore, The side of rhombus = 4cm .
Also the diagonals are 5(4) and 12(4) :- 20 , 48 respectively.
Similar questions