Question

The length of a rectangle is 4 cm more than the width. If the length were to be decreased by 5 cm and width decreased by 2 cm, the perimeter would be 18cm. Calculate the dimensions of the rectangle?

Answer 1

Hint: To solve these types of questions, we need to form equations according to the given questions. The number of equations and the number of different variables we need to use equals the number of conditions, we are given.

Complete step by step solution:
Here, we are asked to find the dimensions of the rectangle using the given two conditions, the first condition states that, length is 4 cm more than the width, and the second condition states that if the length is decreased by 5 cm and width is decreased by 2, the perimeter would be 18 cm.
As we are given two conditions, we need to take two variables to make the equations. Let the length and width of the rectangle are \[x\ and\ y\] respectively.
According the first condition, we have
\[\Rightarrow x=y+4\]
Now, according to the second condition, the new length and width in this case are \[x-5\And y-2\]. The perimeter of the rectangle equals twice the sum of length and width.
\[\begin{align}
  & \Rightarrow 2\left( x-5+y-2 \right)=18 \\
 & \Rightarrow x+y-7=9 \\
 & \Rightarrow x+y=16 \\
\end{align}\]
We formed two-equation according to the given conditions. We can find the two numbers by solving these two equations. The first equation we formed is \[x-y=4\], and the second is \[x+y=16\].
We can easily solve these two equations, by solving them we get \[x=10\And y=6\]

Note:We can check if the answer is correct or not by verifying the condition. From the first condition the difference between the length and width should be 4, as these values satisfy this condition the solution is correct.