Question

Statement I: The length of a rectangle is 10 cm more than its breadth. If the perimeter is 40cm then area of a rectangle is 75 sq.cm

Statement II: Area of rectangle 2(l + b) sq.cm and perimeter lb cm


(a) Both the statement I and II are correct
(b) Both the statement I and II are incorrect
(c) Statement I is correct and statement II is incorrect
(d) Statement I is incorrect and statement II is correct​

Answer 1

Answer:

(c) Statement I is correct and statement II is incorrect

Step-by-step explanation:

Statement I:

Given that:

• The length of a rectangle is 10 cm more than its breadth.
• Perimeter of a rectangle = 40 cm
• Area of a rectangle = 75 cm²

Let the Breadth be x cm.

Then, Length = (x + 10) cm

Formula:

• Area of rectangle = lb sq. unit
• Perimeter of rectangle = 2(l + b) unit

Where, l = Length and b = Breadth

According to the question:

→ 2(x + 10 + x) = 40

→ 2x + 20 + 2x = 40

→ 4x + 20 = 40

→ 4x = 40 - 20

→ 4x = 20

→ x = 20/4

→ x = 5

• Length = (x + 10) cm = (5 + 10) cm = 15 cm
• Breadth = x = 5 cm

Finding the area of rectangle:

• Area of rectangle = (15 × 5) cm²
• Area of rectangle = 75 cm²

In this statement everything is correct.

Statement II:

Area of rectangle = 2(l + b) sq. cm

But, Area of rectangle is lb sq. cm.

Perimeter = lb cm

But, Perimeter is 2(l + b) cm.

In this statement both the formula are incorrect.

Answer 2

Answer:

Given :-

• Length is 10 cm more than breadth
• Perimeter = 40 cm
• Area = 75 cm²

To Find :-

Whether it's correct or not.

Solution :-

As we know that

• Perimeter = 2(l + b)

Let the breadth be a and Length be a + 10

40 = 2(a + 10 + a)

40 = 2a + 20 + 2a

40 = 4a + 20

40 - 20 = 4a

20 = 4a

20/4 = a

5 = a

Breadth = 5 cm

Length = 10 + 5 = 15 cm

Now,

• Area = Length × Breadth

Area = 15 × 5

Area = 75 cm²

Hence, Statement I is correct.

Now,

Above we concluded that,

Area of rectangle = Length × Breadth

And we know rectangle has two length and two breadth

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Perimeter = L + L + B + B

Perimeter = 2(l + b)

Hence, It is wrong

Therefore :-

Option C is correct