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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 $$cm$$).


Solution

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.

Maths

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