Question

The side of a rectangle are x and x+5 .If there Perimeter is 65cm, find the area of rectangle.​

Answer 1

Answer :

• Area of rectangle is 257.8125 cm²

Given :

• The side of a rectangle are x and x + 5
• Perimeter is 65cm

To find :

• Area of rectangle

Solution :

Given,

• Length of rectangle is x
• Breadth of rectangle is x + 5
• Perimeter of rectangle is 65

As we know that

• Perimeter of rectangle is 2(l + b)

Where,

• l is length of rectangle
• b is breadth of rectangle

→ Perimeter of rectangle = 2(l + b)

→ 65 = 2(x + x + 5)

→ 2(2x + 5) = 65

→ 4x + 10 = 65

→ 4x = 65 - 10

→ 4x = 55

→ x = 55/4

→ x = 13.75 cm

Length = x

→ Length = 13.75cm

Breadth = x + 5

→ Breadth = 13.75 + 5 = 18.75cm

Finding the area of rectangle :

We know that

• Area of rectangle = length × breadth

→ Area of rectangle = 13.75 × 18.75

→ Area of rectangle = 257.8125 cm²

Hence , Area of rectangle is 257.8125 cm²

Verification :

→ Perimeter of rectangle = 2(l + b)

→ 65 = 2(13.75 + 18.75)

→ 65 = 2(32.5)

→ 65 = 65

Hence , Verified

Answer 2

To find :  area of rectangle.

Given : length = $x + 5$ and breadth = $x$

             Perimeter = $65 \ cm$

Solution :

• According to question we are given that length and breadth of rectangle are $x$ and $x + 5$  respectively. We have to find area of field.
• Perimeter = $2 ( l + b )$
• $65 = 2 ( x + 5 + x) \\65 = 2 (2x + 5 ) \\65 = 4x + 10 \\4x = 55 \\x = \frac{55}{4} \\x = 13.75$
• Therefore , breadth = $x = 13.75 \ cm$ and

                           length = $x + 5 = 13.75 + 5 = 18.75\ cm$

• To find area we use following formula -

        Area of rectangle $=l \times b$

• Substituting the values we get,

       Area = $18.75 \times 13.75$

               $= 257.8125 \ cm ^{2}$

Hence, area of rectangle is $257.8125 \ cm ^{2}$ .