Question

the length of a rectangular plot of land is twice it's breadth. If the perimeter of the land be 100 meters then find its area​

Answer 1

Answer:

$\boxed{\sf Area \ of \ rectangular \ plot = \frac{5000}{9} \: {m}^{2}}$

Given:

Length of rectangular plot = Twice breadth of rectangular plot

Perimeter of rectangular plot = 100 m

To Find:

Area of rectangular plot

Step-by-step explanation:

Let breadth of rectangular plot be 'b' m

So,

Length of rectangular plot = (2b) m

$\sf \implies Perimeter \: of \: rectangular \: plot =2(length + breadth) \\ \\ \sf \implies 100 = 2(2b + b) \\ \\ \sf \implies 100 = 2(3b) \\ \\ \sf \implies 100 = 6b \\ \\ \sf \implies 6b = 100 \\ \\ \sf \implies b = \frac{100}{6} \\ \\ \sf \implies b = \frac{50}{3} \: m$

$\sf Therefore, \\ \sf Length \: of \: rectangular \: plot = 2b \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times \frac{50}{3} \\ \\ \sf\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{100}{3} \: m \\ \\ \sf Breadth \: of \: rectangular \: plot = b \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{50}{3} \: m$

So,

$\sf Area \: of \: rectangular \: plot = Length \times Breadth \\ \\ \sf = \frac{100}{3} \times \frac{50}{3} \\ \\ \sf = \frac{5000}{9} \: {m}^{2}$

Answer 2

$\huge\star\bold\red{ANSWER}$

$\bold\red{Given:-}$ L=2B

perimeter=>100m

$\bold\red{To}$ $\bold\red{Find:-}$ Area=?

$\bold\red{Solution:-}$

As we know, perimeter=2(L+B)

Now, 2(L+B)= 100cm

=>2(2B+B)=100

=>2(3B)=100

=>6B=100

=>B=$\frac{100}{6}$

=>B=$\frac{50}{3}$m

then, L=2B=2×$\frac{50}{3}$=$\frac{100}{3}$m

Now, As we know Area=L×B

=>$\frac{100}{3}$×$\frac{50}{3}$

=> $\frac{5000}{9}$

=> 555.55555......(556m²).....ans.....

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