Question

the area of a rectangle field is 456 sq.m and its length is 24m. find the breadtg of the fireld and the cost of fencing at the rate of 8.50 per metre​

Answer 1

ɢɪᴠᴇɴ:

⇝Area of field = 456m²

⇝Length of field = 24m

⇝Rate of cost fencing = 8.50 per metre

ᴛᴏ ғɪɴᴅ:

⇝Breadth and cost of fencing the rectangular field.

• ( We need to find Area of rectangular field)

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sᴏʟᴜᴛɪᴏɴ:

⇝Area of rectangle = Length × Breadth

456= 24 × x

x= 456/24

x=19m

Breadth of the given field is 19 m.

• (Now calculating Perimeter)

⇝Perimeter= 2(Length+Breadth)

⇝Perimeter= 2(24+19)

⇝2×43

Perimeter= 86m

Cost of fencing= Rate×Perimeter

86×8.50

Cost of fencing= ₹731

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Answer 2

Answer :-

• The breadth of the field is 19 m.

• The cost of fencing the field is 731.

Given :-

• The area of a rectangular field is 456 m².

• It's length is 24 m.

To find :-

• The breadth of the field.
• The cost of fencing it at the rate of 8.50 per metre.

Step-by-step explanation :-

• In this question, the area and the length of a rectangular field has been given to us. We have to find it's breadth and the cost of fencing it at the rate of 8.50 per metre. For this, we will first find the breadth of the field using the area and length. Then we will find the perimeter of the field using the length and breadth, because fencing can only be done on the boundaries, so we don't have to find the area. Finally, we will use the perimeter to find the cost of fencing the field at 8.50 per metre.

Calculations :-

We know that :-

$\underline{\boxed{\sf Area \: of \: a \: rectangle = Length \times Breadth.}}$

Here,

• Area = 456 m².
• Length = 24 m.

• Let the breadth be b.

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$\underline{\underline{\mathfrak{Substituting \: these \: values \: in \: the \: formula,}}}$

$\boxed{ \tt 456 = 24 \times b}$

Multiplying 24 by b,

$\boxed{ \tt456 = 24b}$

Transposing 24 from RHS to LHS, changing it's sign,

$\boxed {\tt\dfrac{456}{24} = b}$

Dividing 456 by 24,

$\overline{\boxed{ \tt19 \: m = b.}}$

• Hence, the breadth of the field is 19 m.

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• Now, let's find the perimeter of the field using this information and use it to find the cost of fencing it at 8.50 per metre.

We know that :-

$\underline{ \boxed{ \sf Perimeter \: of \: a \: rectangle = 2 \: (L + B)}}$

Here,

• Length = 24 m.
• Breadth = 19 m.

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$\underline{\underline{\mathfrak{Substituting \: these \: values \: in \: the \: formula,}}}$

$\boxed{ \tt Perimeter = 2 \: (24 + 19)}$

Adding the numbers inside the brackets,

$\boxed{ \tt Perimeter =2 \: (43)}$

Removing the brackets,

$\boxed{ \tt Perimeter = 2 \times 43}$

Multiplying the numbers,

$\overline{\boxed{ \tt Perimeter = 86 \: m}}$

• The perimeter of the field is 86 m.

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• So, now to fence the field, we have to fence 86 m.

• For fencing 1 metre, we need 8.50.

• Thus, the cost of fencing the whole field (86 m) is :-

$\overline{ \boxed{ \tt 86 \times 8.50 = Rs \: 731.}}$