Question

ESSAY TYPE
2. The ratio of the length and breadth of a
rectangular field is 3:2 and its area is 11094
sq m. What will be the cost of fencing the
field at the rate of 2.50 per metre?
TE​

Answer 1

GIVEN

The ratio of the length and breadth of a

rectangular field is 3:2 and its area is 11094 sq m.

TO FIND

What will be the cost of fencing the

field at the rate of 2.50 per metre?

SOLUTION

• Area of rectangle = 11094 m²

✒ According to the given condition

✞ Let the length be 3x and breadth

be 2x

Area of rectangle = 11094

➡ length × breadth = 11094

➡ 3x*2x = 11094

➡ 6x² = 11094

➡ x² = 11094/6

➡ x² = 1849

➡ x = √1849

➡ x = ± 43

★ Length and breadth never in negative

Hence,

Length = 3x = 3 × 43 = 129 m

Breadth = 2x = 2 × 43 = 86 m

_____________________

✒Now, Perimeter of rectangle

➡ 2(Length + breadth)

➡ 2(129 + 86)

➡ 2 × 215 = 430 m

Cost of fencing 1m field = Rs.2.50

Cost of fencing 430m field

= Rs.2.50*430 = Rs.1075

_____________________

Answer 2

✧ Given:-

• Ratio of length and breadth:- 3:2

• Area of rectangular field:- 11094m²

✧ To find:-

• Cost of fencing field at the rate of 2.50 per metre?

✧ Solution:-

• Area:- 11094m²

• Ratio of length and breadth:- 3:2

$\implies$ Let's the length be 3x and breadth be 2x.

• Area of rectangle = Length × Breadth

• 11094 = (3x) × (2x)

• 11094 = 6x²

• $\sf{ \cancel{\dfrac{11094}{6}}}$ = x²

• 1849 = x²

$\implies$ Taking sqrt. both side:-

• $\sf{ \sqrt{1849}}$ = $\sf{ \sqrt{x^2}}$

• $\large\bold{\underline{\boxed{\sf{\red{ \dag \; x = 43}}}}}$

★ Putting value of x in 3x and 2x :-

• 3x = 3 × 43 = 129m

$\implies$ Hence, length of rectangular field is 129m.

• 2x = 2 × 43 = 86m

$\implies$ Hence, breadth of rectangular field is 86m.

★ Now, we should find the perimeter of rectangular field:-

Perimeter of rectangle :- 2( length + breadth)

• 2( 129 + 86)

• 2 × 215

• $\large\bold{\underline{\boxed{\sf{\red{ \dag \; 430 m}}}}}$

✶ Given that, cost of fencing 1m field :- 2.50 Rs.

✶ Cost of fencing 430m field :- 2.50 × 430

• $\large\bold{\underline{\boxed{\sf{\red{ \dag \;1050 \; Rs.}}}}}$

$\rule{200}{2}$