The area of a rhombus is equal to the area of triangle whose base and the corresponding altitude are 24.8 cm and 16.5 cm respectively.If one of the diagonals of the rhombus is 22 cm, find the length of the other diagonal.

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Solution

Base of triangle (b)=24.8 cm and altitude (h)=16.5 cm

$∴ A r e a o f t r i a n g l e = \frac{1}{2} \times b a s e \times h e i g h t = \frac{1}{2} b h = \frac{1}{2} \times 24.8 \times 16.5 c m^{2} = 204.6 c m^{2} ∴ A r e a o f r h o m b u s = 204.6 c m^{2} L e n g t h o f o n e d i a g o n a l (d_{1}) = 22 c m ∴ S e c o n d d i a g o n a l (d_{2}) = \frac{A r e a \times 2}{d_{1}} = \frac{204.6 \times 2}{22} = 18.6 c m$

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The area of a rhombus is equal to the area of triangle whose base and the corresponding altitude are 24.8 cm and 16.5 cm respectively.If one of the diagonals of the rhombus is 22 cm, find the length of the other diagonal.

Base of triangle (b)=24.8 cm and altitude (h)=16.5 cm ∴ Area of triangle=12×base×height=12bh=12×24.8×16.5 cm2=204.6 cm2∴ Area of rhombus=204.6 cm2Length of one diagonal (d1)=22 cm∴ Second diagonal (d2)=Area×2d1=204.6×222=18.6 cm