Question

I
- The cost of turfing a rectangular field at 85 paise per square metre is 624.75. Find the perimeter and
area of the field if its sides are in the ratio 5: 3.​

Answer 1

Step-by-step explanation:

Length of rectangle is 30 m.

Breadth of rectangle is 20 m.

Step-by-step explanation:

Given:-

Perimeter of rectangle is 100 m.

To find:-

Length of rectangle.

Breadth of rectangle.

Solution:-

Let, Breadth of rectangle be x m.

And, Length of rectangle be x + 10 m.[We take length be x + 10 m because it is given that length is 10 m more than Breadth.]

We know,

Perimeter of rectangle = 2(Length + Breadth)

Put the values:

\longrightarrow⟶ 100 = 2×(x + 10 + x)

\longrightarrow⟶ 100 = 2x + 20 + 2x

\longrightarrow⟶ 100 = 4x + 20

\longrightarrow⟶ 100 - 20 = 4x

\longrightarrow⟶ 80 = 4x

\longrightarrow⟶ x = 80/4

\longrightarrow⟶ x = 20

Verification:-

\longrightarrow⟶ 100 = 2×(x + 10 + x)

Put x = 20

\longrightarrow⟶ 100 = 2×(20 + 10 + 20)

\longrightarrow⟶ 100 = 2×(30 + 10)

\longrightarrow⟶ 100 = 60 + 10

\longrightarrow⟶ 100 = 100

\boxed{\sf Hence \: Verified.}

HenceVerified.

We have taken,

Breadth be x. So, Breadth of rectangle is 20 m.

Length be x + 10 = 20 + 10 = 30. Thus, Length of rectangle is 30

Answer 2

☆ Solution ☆

Given :-

• The cost of turfing a rectangular field at 85 paise per square metre is 624.75 .

To Find :-

• The perimeter and area of the field if its sides are in the ratio 5: 3 .

Step-by-Step-Explaination :-

Let the ratios be 5x and 3x

As we know that :-

Area of rectangle = l × b

Putting the respective value,

Area of rectangle = 5x × 3x

Area of rectangle = 15x²

According to the condition,

Area of rectangular field × 85/100 = Rs 624.75

Therefore,

15x² × 85/100 = 624.75

x² = 624.75 × 100/15 × 85

x² = 49

x = 7

Hence,

The dimension of rectangle are 5 × 7 = 35 m and 3 × 7 = 21 m

Now,

As we know that :-

Perimeter of rectangle = 2 ( l + b )

Putting the respective value,

Perimeter of rectangle = 2 ( 35 + 21 )

Perimeter of rectangle = 2 × 56

Perimeter of rectangle = 112 m

Hence,

The perimeter of rectanglular field = 112 m