Question

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 22cm , find the length of other diagonal.

Answer 1

area of rhombus= area of triangle

Area of triangle = ½× base × height
= ½×24.8×16.5
= 204.6cm²

area of rhombus = ½× diagonal1× diagonal 2
204.6 = ½× 22× diagonal2

$\frac{204.6 \times 2}{22} = diagonal 2$
therefore,

the other diagonal = 18.6 cm

Answer 2

Area of triangle= 1/2 × base× height
= 1/2 × 24.8cm× 16.5 cm
= 12.4cm× 16.5 cm= 204.6cm^2
As areas are equal
Area of rhombus= 1/2 × d1×d2
204.6cm^2= 1/2 × 22cm×d2
204.6cm^2= 11cm×d2
204.6cm^2/ 11cm= d2
18.6cm= diagonal
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