a rohmbus of side equal to 65 cm has an area of 2016 cm find the diagonals - Maths -

Question

a rohmbus of side equal to 65 cm has an area of 2016 cm find the
diagonals

ramandeep.singh · Accepted Answer

Let the diagonals of the rhombus be x cm and y cm.

$∴ A r e a = \frac{1}{2} x y = 2016 c m^{2} \Rightarrow x y = 2 \times 2016 c m^{2} = 4032 c m^{2} (1)$

$s i d e = 65 c m \Rightarrow \sqrt{(\frac{x}{2})^{2} + (\frac{y}{2})^{2}} = 65 c m \Rightarrow \frac{1}{2} \sqrt{x^{2} + y^{2}} = 65 c m \Rightarrow \sqrt{x^{2} + y^{2}} = 130 c m ∴ x^{2} + y^{2} = (130 c m)^{2} = 16900 c m^{2} (2)$

Now,

$(x + y)^{2} = x^{2} + y^{2} + 2 x y = 16900 c m^{2} + 8064 c m^{2} = 24964 c m^{2} ∴ x + y = 158 c m (3) (x - y)^{2} = x^{2} + y^{2} - 2 x y = 16900 c m^{2} - 8064 c m^{2} = 8836 c m^{2} ∴ x - y = 94 c m (4)$

On solving equations (3) and (4), we get

x = 126 cm

y = 32 cm

a rohmbus of side equal to 65 cm has an area of 2016 cm.find the diagonals.