Question

= 3281.25
tercise 15.1
The length of a rectangular-shaped label is 1 centimetre more than twice the width. The perimeter
- 110 centimetres. Find the area of the rectangle.​

Answer 1

666cm².

Step-by-step explanation:

Let,

Width = x.

Length = 1 + 2x.

Perimeter of rectangle = 2(l + w).

Putting known values in the formula

➻ 110 = 2(1+2x + x).

Adding 2x and x

➻ 110 = 2(1+3x).

Multiplying 1 and 3x by 2

➻ 110 = 2 + 6x.

Bringing 2+6x to LHS

➻ 2 + 6x = 110.

Subtracting 2 from 110

➻ 6x = 110 - 2.

It can be written as

➻ 6x = 108.

Dividing 108 by 6 to find the value of x

➻ x = 108/6.

On cancelling we get

➻ x = 54/3.

Bringing this fraction into the simplest form and again cancelling

➻ x = 18.

Therefore,

Width = x = 18cm.

Length = 1+2x = 1+2(18) = 1+36 = 37cm.

Now, calculating area of the rectangle

Area of rectangle = Length × Width

Area of rectangle = 18 × 37

Area of rectangle = 666cm².

Answer 2

To Find :

The Area of the rectangle given .

Given :

• Length of Rectangle is 1 centimeter more than twice of the width .
• Perimeter of the rectangle = 110 cm

Formula To be Applied :

We will here use these formula related to rectangle :

1] Perimeter of rectangle:

P = 2(l+b)

2] Area of rectangle:

Area = l×b

Let's Assume :

Let's Assume that the breadth of the rectangle is 'x'.

So, Length = 1+2breadth

or, Length = 1+2x = 2x+1

Process:

We will first Assume the length and breadth of the rectangle. Then with the formula of perimeter of rectangle, we will find the value of x and then find the length and breadth.

Through these values, we can find the area of the rectangle.

Solution :

Breadth = x

Length = 2x+1

So, perimeter = 2(l+b)

$\implies \tt{p = 2(x + 2x + 1)}$

$\implies \tt{110 = 2(3x + 1)}$

$\implies \tt{110 = 6x + 2}$

$\tt{ \implies 6x = 110 - 2}$

$\implies \tt{x = \frac{108}{6} }$

$\implies \tt{x = 18}$

Hence, Breadth = x = 18 cm

Length = 2x+1 = 37 cm

Hence, Area = l×b

$\implies \tt{area = 18 \times 37}$

$\red{ \underline{ \boxed{ \tt{ \therefore area = 666 \: c {m}^{2} }}}}$

Hence, Area of rectangle = 666 cm ²

__________________________

Additional Information :

These are some formulas related to mensuration:

• Area of rectangle = l×b
• Area of Square = Side²
• Area of Circle = (pi)r²
• Area of Triangle (Simple) = ½×base×Hieght
• Area of triangle (Heron's)

$\tt{area = \sqrt{s(s - a)(s - b)(s - c)}}$

• Perimeter of rectangle = 2(l+b)
• Perimeter of Square = 4×side
• Perimeter of circle = 2(pi)r
• Perimeter of triangle = a+b+c