Question

Area of a rectangle is 51.2 dm2 and the sides are in the ratio 5:4 find its perimeter

Answer 1

Answer:

Perimeter = 28.8dm

Step-by-step explanation:

let the sides be 5x & 4x

$\implies$ $Area\:of\: rectangle\:=\:l×b$

$\implies$ $51.2\:=\:5x\:×\:4x$

$\implies$ $51.2\:=\:20\:x^{2}$

$\implies$ $\large\frac{51.2}{20}\:=\:x^{2}$

$\implies$ $2.56\:=\:x^{2}$

$\implies$ $x\:=\:\sqrt{2.56}$

$\implies$ $x\:=\:1.6$

Substitute x in sides :

5x = 5(1.6) = 8 dm

4x = 4(1.6) = 6.4dm

$Perimeter\:of\:rectangle\:=\:2(l+b)$

$\implies$ $P\:=\:2(8\:+\:6.4)$

$\implies$ $P\:=\:2(14.4)$

$\implies$ $\large\boxed{Perimeter\:=28.8\:dm}$

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Answer 2

Answer:

28.8 dm

Step-by-step explanation:

We have, area of the rectangle= 51.2 dm^2

Ratio of the sides= 5:4

Let the sides are 5x and 4x, then using the formulae for the rectangle's area(Length*Breadth);

=> 5x*4x=51.2 dm^2

=> 20x^2=51.2 dm^2

=> x^2=51.2/20

=> x=✓2.56

=> x=1.6

So, Length=5x=8 dm

Breadth=4x=6.4

therefore, perimeter of a rectangle= 2(L+B)

=2(8+6.4)

=2(14.4)

=28.8 dm