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

• A. $side-26cm,diagonals-20cm,48cm$
• B. $side-26cm,diagonals-40cm,96cm$
• C. $side-25cm,diagonals-20cm,48cm$
• D. none of the above

Answer 1

Answer: (A)

$side-26cm,diagonals-20cm,48cm$

Its perimeter is $104cm$
Perimeter $=4xside=104$
=> side =$26cm$
The diagonals of a rhombus are in the ratio $5:12.$
Let diagonals are $5x$ and $12x$
Diagonals of rhombus are perpendicular to each other, so by applying Pythagoras theorem
=> $a^2=(\frac{5x}{2}{)}^2+(\frac{12x}{2}{)}^2$
=> ${26}^2=\frac{169x^2}{4}$
=> $x=4$
Diagonals are $5x=20cm$ and $12x=48cm$