Question

a rohmbus sheet ,whose perimeter is 32m and one diagonal is 10 m long ,is painted on both sides at the rate of rs 5per m² find the cost of painting

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Answer 1

Step-by-step explanation:

Perimeter = 32 m,

So, length of a side =32/4=8m,

and Diagonal of a rhombus = 10m,

As, we know that,

The halves of diagonals and a side of a rhombus from a right angled triangle with side as hypotenuse.

Let the length of the other diagonal =2x.

x^2+(10/2)^2= 8^2 =x^2+25=64x

2

+(10/2)

2

=8

2

=x

2

+25=64

x^2=64-25 = 39x

2

=64−25=39

x=\sqrt { 39 } x=

39

The measure of the another diagonal of the rhombus = 2*\sqrt { 39 } =2\sqrt { 39 } m

So, Area of the rhombus =1/2*Diagonal of a rhombus*Measure of the another diagonal

A=\frac { 1 }{ 2 } \times 10\times 2\sqrt { 39 }A=

2

1

×10× 2

39

A=62.45 m^2A=62.45m

2

painted on both sides at the rate of Rs 5 per m2

Cost = area of both side*5=2*62.45*5=624.50 Rs

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