Question

the side of a rectangle Park are in the ratio 9 : 7 if its area is 1728 square metre find it perimeter cost of fencing it at rate of rupees 40 per month​

Answer 1

$\blue\bigstar$ Correct Question:

• If the sides of a rectangular park are in the ratio 9 : 7 with an area of 1575 m². Then find the cost of fencing if the rate is ₹40 per meter.

$\pink\bigstar$Answer:

• The cost of fencing will be ₹6400

$\green\bigstar$Given:

• The side of a rectangular park are in the ratio 9 : 7
• Area of the rectangular park = 1575m²

$\blue\bigstar$To find:

• Cost of fencing if it's rate is ₹40 per metre

$\pink\bigstar$ Solution:

$\because$the sides are unknown, let's take the sides of the rectangular park in the form of x.

$\therefore$ The sides are 9x and 7x.

Let the length be 9x and breadth be 7x.

We know that :

• Area of the rectangle = (Length) × (Breadth)

Now,

• Length of the rectangular park = 9x
• Breadth of the rectangular park = 7x

Given area of the rectangular park = 1575 m²

Area of the rectangular park in terms of side

= 9x × 7x

= 63x²

$\because$Both are equal,

$\therefore$63x² = 1575 m²

$\implies$ x² = $\dfrac{{1575\: m}^{2}}{63}$

$\implies$x² = 25m²

$\implies$x = √25m²

$\implies$$\boxed{x \: = 5m}$

$\therefore$The sides are:

• 9x = 9 × 5 = 45m
• 7x = 7 × 5 = 35m

Now for fencing, we need to find out the perimeter of the rectangular park.

$\bigstar$We know that :

• Perimeter of a rectangle = 2( Length + Breadth)

So by substituting the values of length and breadth, we get :

Perimeter of the rectangular park = 2( 45m + 35m )

$\implies$Perimeter of the rectangular park = 2( 80m )

= 160m

Given rate of fencing per meter = ₹40

Rate of fencing of the rectangular park

= ₹40 (160 )

= ₹6400

$\therefore$ The cost of fencing will be ₹6400.

$\green\bigstar$ Concepts Used:

• Assumption of unknown sides
• Area of the rectangle = (Length) × (Breadth)
• Transposition Method
• Substitution of values
• Perimeter of a rectangle = 2( Length + Breadth)

$\red\bigstar$ Extra - Information:

• Area of a square = (Side)²
• Perimeter of the square = 4 × Side
• Area of a Triangle = $\dfrac{1}{2} Height \times Breadth$
• Perimeter of a triangle = Sum of all sides
• Perimeter of an equilateral triangle = 3(Side)
• Perimeter of an Isosceles Triangle = 2(Same side) + Different side
• Area of a circle = πr²
• Perimeter of a circle = 2πr or πd

Answer 2

$\bigstar$ EXPLAINATION $\bigstar$

• GIVEN

The ratio of the sides of the rectangle is 9:7

Cost of fencing per meter = 40 rupees

Let the sides be 9x and 7x respectively

$\red\star$Area of a rectangle = Length * Breadth

Therefore,

Area of the given rectangle = 9x * 7x = 63x^2

But in the question, they mentioned the area is equal to 1728 m^2

Therefore,

1728 = 63x^2

x^2 = 27.428

x = ±5.237 m

As the side cannot be negative

Therefore,

x = 5.237 m

Length of the rectangle = 9x = 9*5.237 = 47.133 m

Breadth of the rectangle = 7x = 7*5.237 = 36.659 m

$\red\star$Perimeter of a rectangle = 2*(Length + Breadth)

Therefore,

Perimeter of the given rectangle = 2*(47.133 + 36.659) = 167.584 m

Cost of fencing for 167.584 m = 40*167.584 = 6703.36 rupees

$\bigstar$ EXTRA INFORMATION $\bigstar$

i) Area of a triangle = $\frac{bh}{2}$, b is the length of a side of the triangle and h is the length of the perpendicular drawn from the side which is considered as side.

ii) Area of triangle = $\sqrt{s(s-a)(s-b)(s-c)}$, a, b, c are the lengths of the sides of the triangle and s is the semi perimeter of the triangle

$s = \frac{(a+b+c)}{2}$