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 $$=20$$ cmPerimeter of the triangle $$=60$$ cmPerimeter of a rhombus $$=60$$ cm $$=4\times$$ side of rhombus$$\Rightarrow a=15$$ cmDiagonal $$= 24$$ cmDiagonal $$24$$ cm $$= 12$$ cm $$+ 12$$ cm $$=$$ legs of right triangle within rhombus.$$a=15$$ cmSo, $$15^ 2=12^ 2+x^ 2$$$$\Rightarrow x^ 2=81$$$$\Rightarrow x=9$$Diagonal $$=2\times$$ legs of right triangle within rhombus $$=2\times 9=18$$ cm.Maths

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