Question

the length of a rectangular plot exceeds its breath by 5m. if the perimeter of the plot is 142m. find the dimensions of the plot

Answer 1

Given

Length of rectangular plot exceeds it's breadth by 5 m.

Perimeter of plot = 142 m.

To find

Dimensions of plot

Solution

Let the breadth of plot be b m. And, length of plot be (b + 5) m.

We know that,

➥ Perimeter of rectangle = 2(l + b)

Putting values we get :

➪ 142 = 2(b + 5 + b)

➪ 142/2 = 2b + 5

➪ 71 = 2b + 5

➪ 71 - 5 = 2b

➪ 66 = 2b

➪ 66/2 = b

➪ b = 33

Now finding length of plot :

➼ Length of plot = b + 5

➼ Length of plot = 33 + 5

➼ Length of plot = 38 m

Now finding breadth of plot :

➺ Breadth of plot = b

➺ Breadth of plot = 33 m

Therefore,

Dimensions of rectangular plot are 38 m & 33 m respectively.

Answer 2

Answer :

The length of the rectangular plot is 38m and the breadth is 33m

Given :

• The length of a rectangular plot exceeds its breadth by 5m
• The perimeter of the plot is 142m .

To Find :

• The dimensions of the plot.

Solution :

Let us consider the length and breadth of the rectangular plot be x and y

According to First condition :

$\sf{x = y + 5}............(1)$

And the perimeter of the plot is 142m

$\implies \sf{2(x + y) = 142} \\ \implies \sf{x + y = 71} ..........(2)$

Putting the value of x from (1) in (2)

$\sf \implies y + 5 + y = 71 \\ \implies \sf{2y = 71 - 5} \\ \implies \sf{y = \frac{66}{2} } \\ \implies \sf{y = 33}$

Now putting the value of y in (1) we have :

$\sf \implies{x = 33+ 5} \\ \implies \sf{x = 38}$

Thus the length is 38m and the breadth is 33m