Question

the length of rectangular path is 1.5 m times its breadth of perimeter of plot is 180 m then find the area of plot,? ​

Answer 1

In context to questions asked,

We have to determine the value of area of plot

As per questions,

It is given that

The length of rectangle is 1.5 times to the breadth of rectangle.

So, let the breadth of rectangle = X

So, length of rectangle will be = (1.5×x) = 1.5x

As we know that,

$Perimeter = 2(l +b ) \\ = > 180 = 2(x + 1.5x) \\ = > 180 = 5x \\ x = \frac{180}{5} = 36$

So, length and Breadth of rectangle will be

$b = 36 \: m \\ l = 1.5 \times 36 = 54 \: m$

Hence, area of rectangle will be,

$= lb = 36 \times 54 = 1944 \: {m}^{2}$

Answer 2

To find : area of plot .

Given :  length of rectangular path is $1.5$ m times its breadth of perimeter of plot is $180\ m$ .

Solution :

• Let , breadth of rectangle plot be $x$ .
• Then as per given data we know that length of rectangular path is $1.5$ m times its breadth of perimeter of plot is $180\ m$ .
• Therefore , length becomes  $1.5 x$ m .
• Now , to find original length and breadth of plot we use following formula .
• Perimeter of plot = $2 ( l + b)$

        $180 =2 (1.5x + x )\\180 = 3x + 2x \\180 = 5x \\x = 36$

• Now , breadth = $36\ m$ and  length = $1.5 \times 36 =54\ m$

• To find area we use following formula -
• Area of rectangle $=l \times b$  
• Substituting the values we get,
• Area of plot = $54\ m \times 63 \ m$

                             $= 1944\ m^{2}$

Hence, area of rectangular plot is $1944\ m^{2}$  .