Question

The perimeter of a rectangle is 40 cm. The length of the rectangle is more than double its breadth by 2 cm. Find the length and breadth of the rectangle.

Answer 1

Hint: As we can see that we need to find the dimensions of a rectangle and we are given the perimeter here then we will directly use the formula perimeter = 2(length + breadth) and solve the question. Also, as we are given that the length of the rectangle is more than double its breadth by 2 cm therefore; we will have the length as 2b + 2 cm where b is the breadth of the rectangle.

Complete step-by-step answer:
According to the given information to us we have a rectangle whose perimeter is given by 40 cm. Now, we will consider that the breadth of the rectangle be b cm. Since, we are given that the length of the rectangle is more than double its breadth by 2 cm therefore; we get the length as 2b + 2 cm....(i). The figure according to the question is given as,

Now, we will use the formula of the perimeter of the rectangle which is given by perimeter = 2(length + breadth). As the perimeter is 40 cm, length is 2b + 2 cm and breadth is b cm therefore, we have 40 = 2(2b + 2 + b). This results into 40 = 2(3b + 2) and we can further write this equation as 40 = 6b + 4. Therefore, the value of 6b = 40 – 4 or b = $\dfrac{36}{6}$ which after simplifying gives b = 6 cm. Thus, we have the breadth of the rectangle as 6 cm.
Now, we will substitute this value in equation (i) so, we will get the length of the rectangle as 2b + 2 = 2b + 2 or 2(6) + 2. Therefore, we have a length of 14 cm.
Hence, the required values of length and breadth of the rectangle are 14 cm and 6 cm respectively.

Note: The solution becomes easy when the formula of the perimeter is used. This is because the value of the perimeter was given. While drawing the diagram one should take care of the fact that the diagram here should look similar to rectangle only and not square. As we are given centimetres as a unit here so we will check first that the dimensions given to us is also in centimetres or not. After that we will proceed with the question otherwise, we will first make the units the same. If the question asked the dimensions of the rectangle in metres then we will use the conversion 1 metre = 100 centimetre in the last line of the solution and get the desired result.