Question

The perimeter of a rectangular plot is 60 m and area is 200 sq meters. Find its dimensions.​

Answer 1

Given :

• The Perimeter of a rectangular plot = 60 m.

• Area of rectangular plot = 200 m².

To find :

• It's Dimensions =?

Step-by-step explanation:

Area of rectangular plot = 200 m². [Given]

We know that,

Area of Rectangle = length x breadth.

Substituting the values in the above formula, we get,

length x breadth = 200

breath = 200/length

Now,

Putting the value of breadth in Perimeter of rectangle,

We know that,

Perimeter of Rectangle = 2 ( Length + Breadth)

Substituting the values in the above formula, we get,

➮ 2(l+200/l) = 60

➮ 2(l²+200) = 60l

➮ 2l²+400 = 60l

➮ l²+200 = 30l

➮ l²-30l+200 = 0

➮ l²-20l-10l+200 = 0

➮ l(l-20)+10(l-20) = 0

➮ (l+10)(l-20) = 0

Therefore,

Length of rectangular = -10, 20

As we know that,

Distance can never be negative,

So, Length of rectangular plot = 20 m

Now,

Putting the value of length in area of rectangle,

As we know that,

Area of Rectangle = length x breadth

Substituting the values in the above formula, we get,

length x breadth = 200

20 x breadth = 200

breadth = 200/20

breadth = 10 m

Therefore,

Length of the rectangular plot = 20 m

And, Breadth of the rectangular plot = 10 m

Answer 2

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Given :-

perimeter of plot = 60m

area of plot =$200m^2$

To find :-

dimensions of the plot :-

formulae used :-

perimeter of plot = 2(l+b)

area of plot = l x b

step by step explanation :-

perimeter of plot = 2(l+b)

60 = 2(l + b)

l + b = 30 --------------------(i)

area of the plot = l * b

200 = l * b--------------(ii)

$(l+b)^2 = l^2+b^2+2lb$

$30^2 = l^2 + b^2+2*200$

$900= l^2+ b^2+400$

$l^2+b^2= 900-400$

$l^2+b^2= 500$----------------(iii)

$(l-b)^2=l^2 + b^2 -2lb$

$(l-b)^2 = 500- 2*200$

$(l-b)^2 = 100$

$l - b= \sqrt100$

$l-b = 10$---------------------(iv)

adding eq (i) and (iv)

l+b+l-b=30+10

2l=40

l=20m

putting value of l in eq (i)

l+b=30

20+b=30

b=10m

Answers :-

length = 20meter

breadth = 10meter

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