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

So the answer is 1960

Step-by-step explanation:

Ratio of length and breadth is 3:2 (l:b)

Area = l*b = 294

3x * 2x = 294

6x^2 = 294

x^2 = 294/6

x^2 = 49

x= square root of 49

x= +/- 7.

Length and Breadth can not be negative hence x=7

l:b = 3:2 => 3x:2x => 21:14

Area = l*b = 21*14 = 294

Circumference of Rectangle= 2*(l+b)

=2*(21+14)

= 2*35 = 70m

Cost to fence per meter = 28

cost to fence 70m = 28*70

=1960

Answer 2

⠀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.

Stated -

• The sides of rectangle are in ratio of 3:2
• Area of rectangle is 486m²
• Cost of fencing at 1m² is ₹40

To Attain -

• Total cost of fencing at ₹40 m²

Formula to be used -

• Perimeter of rectangle = 2(l + b)

Where -

• L stands for length
• B stands for breadth

Analysis -

⠀In the question, It has been stated that sides of a rectangle are in ratio of 3:2 and the area of rectangle is 486m² also, if cost of fencing m² is ₹40 then what should be the total cost? We will find out the answer by using the formula of perimeter of rectangle. Let's get it!

⠀As we have been given that, the rectangle sides are in ratio of 3 : 2

⠀So, Let's the side be x

⠀

⠀⠀⠀${\underline{\pmb{\bigstar{\sf{ \: According\:to\:the\:question : }}}}}$

$\longrightarrow{\pmb{\sf{\red{Area_{ \:(rectangle)} = {486cm}^{2}}}}}\\\\\\ \longrightarrow\sf{Length \times Breadth = {486cm}^{2}} \\\\\\ \longrightarrow\sf{ \: 3x \: \times 2x = {486cm}^{2}}\\\\\\ \longrightarrow\sf{ {6x}^{2} = {486cm}^{2}} \\\\\\ \longrightarrow \sf{{x}^{2} = \dfrac{486}{6}}\\\\\\ \longrightarrow\sf{ {x}^{2} = 81}\\\\\\ \longrightarrow\sf{x = \sqrt{81} } \\\\\\ \longrightarrow\underline{\boxed{ \pmb{\sf{\red{x = 9}}}}}$

Now,

⠀We have been gotted our required value of x and now only perimeter of rectangle and total cost of fencing are pending. So, Let's do this too! By applying the formula of perimeter of rectangle but before we find the Value of 3x and 2x

So,

• 3x = 3 × 9 = 27cm
• 2x = 2 × 9 = 18cm

Since,

$\:\:\dashrightarrow \pmb{\sf{\red{Perimeter_{\:(Rectangle)} = 2(l+b)}}}\\\\\\ \dashrightarrow\sf{Perimeter = 2 \: (27 + 18)} \\\\\\ \dashrightarrow \sf{Perimeter = 2(45)} \\\\\\ \dashrightarrow \underline{\sf {\red{Perimeter = 90m}}}$

Therefore,

• Cost of fencing per metre = ₹40
• Cost of fencing at 90m = 90 × 40
• Total cost of fencing at 90m = ₹3600

Final Answer -

★ Perimeter of the rectangle is 90m & The cost of fencing at 90m is ₹3600

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