Question

The Perimeter of a Rectangle is 154. Its length is a more than twice its breadth. What is the area? ​

Answer 1

Answer:

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Answer 2

Given :

• Perimeter of a rectangle = 154 units

• Length is a more than twice its breadth

To find :

• Area of the rectangle

Concept :

Here, we have to find the area of the rectangle. So, for that we need the dimensions of the rectangle. To find the dimensions firstly we will assume the length and breadth of the rectangle according to the conditions given in the question. Then by using the formula of perimeter of rectangle we will get their values.

Formula to find area of rectangle :-

• Area of rectangle = l × b

Formula to find the perimeter of rectangle :-

• Perimeter of rectangle = 2(l + b)

where,

• l denotes the length of the rectangle.

• b denotes the breadth of the rectangle.

Solution :

Let the breadth of the rectangle be x metre and the length be one more than twice its breadth, i.e. 2x + 1 metre

→ Perimeter of the rectangle = 2(l + b)

→ Substituting the given values :-

→ 154 = 2(2x + 1 + x)

→ Transposing 2 to the left hand side :-

→ 154 ÷ 2 = 2x + 1 + x

→ 77 = 2x + 1 + x

→ 77 = 3x + 1

→ 77 - 1 = 3x

→ 76 = 3x

→ Transposing 3 to the left hand side :-

→ 76 ÷ 3 = x

→ 25.3 = x

→ On rounding off, we get :-

→ 25 = x

Therefore, the value of x = 25

Substituting the value of x in he dimensions of rectangle :-

LENGTH :-

→ Length = 2x + 1

→ Length = 2 × 25 + 1

→ Length = 50 + 1

→ Length = 51 m

BREADTH :-

→ Breadth = x = 25 m

Therefore, the dimensions of the rectangle are 51 m and 25 m.

Now, calculating the area of the rectangle :-

→ Area of rectangle = l × b

→ Area of rectangle = 51 × 25

→ Area of rectangle = 1275

Therefore, the area of rectangle = 1275 square units.