Question

The lengths of the diagonals of a rhombus are in the ratio 1:2. The length of its side is 35 cm. Find the area of the rhombus.

Answer 1

Answer:

area of rhombus= d1×d2/2

=1x×2x/2

=2x²/2

=x²

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Answer 2

Answer:

980cm2

Step-by-step explanation:

Length of a side of a rhombus given the diagonals = $\sqrt{(d1^2/4) + (d2^2/4)}$

=> Taking the ratio 1:2 as x and 2x,

= $\sqrt{(x^2/4) + (4x^2/4)}$

=$\sqrt{(x^2/4) + x^2}$

=$\sqrt{x^2(1/4 + 1)}$

=$\sqrt{x^2(5/4)}$

= Length of side = $x (\sqrt{5}/2)$ = 35

= x = $(2/\sqrt{5}) * 35$

    = $(2/\sqrt{5}) * (\sqrt{5} * \sqrt{5} * 7 )$

    =$14\sqrt{5}$

Area = $(1/2)*(d1*d2)$

        =$(1/2) * (x * 2x)$ = $(1/2) * (14\sqrt{5} * 28\sqrt{5} )$

        =$14\sqrt{5}*14\sqrt{5}$

        =$196 * 5$

        = $980 cm^{2}$

        =