Question

The sides of a rectangle are in the ratio
3:2. If the area is 486 sqm, find the cost
of fencing it at 40 per metre.​

Answer 1

Answer:

if the area is 486 sq m , find the cost of fencing in at rs.40 per metre.

2. See answers.

let the side be x ratio of the sides are 3:2so the sides are 3x and 2x area of rectangle=l×b

Answer 2

Answer:

• The cost of fencing is Rs. 3,600.

Step-by-step explanation:

Given :-

• The sides of a rectangle are in the ratio of 3 : 2.
• The area of the rectangle is 486 m².
• Rate of fencing is 40 per metre.

To find :-

• The cost of fencing at the rate of 40 per metre.

Solution :-

In order to find the cost of fencing, it is important to have it's perimeter. But we aren't given the dimensions of the rectangle to find it's perimeter. So to find the dimensions of the rectangle, firstly, let us assume the length of the rectangle be 3x. So the value of the breadth of the rectangle will be 2x, since the ratio of the length and breadth of the rectangle is 3 : 2. So, by using the formula of area of the rectangle we will find out the value of x. After that, we will confirm the value of x by verifying it. And then, by putting the value of x in the assumed dimensions we will find out the dimensions of the rectangle. Then, by using formula of perimeter of rectangle we will find out it's perimeter. And at last, we will find out the cost of fencing. Let's do it!

Given :

• Length of rectangle = 3x.
• Breadth of rectangle = 2x.
• Area of rectangle = 486 m².

According to the question :-

$\sf \longrightarrow {Area\ of\ rectangle\ =\ length \times breadth}$

• On substituting the values,

$\sf \longrightarrow {486\ =\ (3x) \times (2x)}$

$\sf \longrightarrow {486\ =\ 6x^2}$

$\sf \longrightarrow {\dfrac{\cancel{486}}{\cancel 6}\ =\ x^2}$

$\sf \longrightarrow {81\ =\ x^2}$

$\sf \longrightarrow {\sqrt{81}\ =\ x}$

$\sf \longrightarrow {9\ =\ x}$

$\sf \longrightarrow {\underline{x\ =\ 9}}\ \bigstar$

Now we have the value of x as 9. So, before proceeding to the next step, firstly, let us confirm the value of x by verifying it.

$\sf \longrightarrow {Area\ of\ rectangle\ =\ length \times breadth}$

$\sf \longrightarrow {486\ =\ (3x) \times (2x)}$

• Putting x = 9, we get,

$\sf \longrightarrow {486\ =\ (3 \times 9) \times (2 \times 9)}$

$\sf \longrightarrow {486\ =\ (27) \times (18)}$

$\sf \longrightarrow {486\ =\ 486}$

$\sf \longrightarrow {\underline{LHS\ =\ RHS}}\ \bigstar$

Now, LHS is equal to the RHS. Hence, the value of x is correct. So, now we will find out the dimensions of the rectangle by putting the value of x in the assumed dimensions.

• Length : 3x = 3(9) = 27 m.
• Breadth : 2x = 2(9) = 18 m.

Now we have the dimensions of the rectangle. So now, we will find out the perimeter of the rectangle.

$\sf \longrightarrow {Perimeter\ of\ rectangle\ =\ 2(length\ +\ breadth)}$

• On substituting the values,

$\sf \longrightarrow {2(27\ +\ 18)}$

$\sf \longrightarrow {2(45)}$

$\sf \longrightarrow {2 \times 45}$

$\sf \longrightarrow {\underline{90\ m}}\ \bigstar$

Now we know the perimeter of the rectangle. So at last, we will find out the cost of fencing.

$\sf \longrightarrow {Cost\ of\ fencing\ =\ Rate\ of\ fencing \times Perimeter\ of\ rectangle}$

$\sf \longrightarrow {40 \times 90}$

$\sf \longrightarrow {\underline{3,600}}\ \bigstar$

∴ Hence, the cost of fencing is Rs. 3,600.