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Question

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

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Solution

Side of the triangle =20 cm
Perimeter of the triangle =60 cm
Perimeter of a rhombus =60 cm =4× side of rhombus
a=15 cm
Diagonal =24 cm
Diagonal 24 cm =12 cm +12 cm = legs of right triangle within rhombus.
a=15 cm
So, 152=122+x2
x2=81
x=9
Diagonal =2× legs of right triangle within rhombus =2×9=18 cm.

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