Question

The perimeter of a rhombus with one diagonal $24cm$ long is the same as the perimeter of an equilateral triangle with side $20cm$. Find the length of the other diagonal (in $cm$).

Answer 1

Side of the triangle $=20$ cm
Perimeter of the triangle $=60$ cm
Perimeter of a rhombus $=60$ cm $=4\times$ side of rhombus
$\Rightarrow a=15$ cm
Diagonal $=24$ cm
Diagonal $24$ cm $=12$ cm $+12$ cm $=$ legs of right triangle within rhombus.
$a=15$ cm
So, ${15}^2={12}^2+x^2$
$\Rightarrow x^2=81$
$\Rightarrow x=9$
Diagonal $=2\times$ legs of right triangle within rhombus $=2\times 9=18$ cm.