Question

\[4{\text{ }}\left( {x - 2} \right)\] metres of rope is used to fence the rectangular enclosure shown in the Fig. Find x.

Answer 1

Hint: To solve this question, we will need the breadth of the rectangle. As the area is given, we will obtain breadth using the area of the rectangle. Afterwards we will obtain the value of x using the formula of perimeter of the rectangle.

Complete step-by-step answer:

Step 1: We have been given area of rectangle \[ = {\text{ }}225{m^2}\]
And also, length of rectangle \[ = {\text{ }}25m\]
Now, let the breadth of the rectangle be b
We know that, Area of rectangle \[ = {\text{ }}(Length\; \times Breadth)\]
On putting the value in the above formula, we get
 $ \begin{gathered}
  225 = (25 \times b) \\
  b = \dfrac{{225}}{{25}} = 9m \\
\end{gathered} $
Thus, breadth of the rectangle is \[9m.\]
Step 2: Now, we have been given the length of rope used to measure rectangle \[ = {\text{ }}4{\text{ }}\left( {x - 2} \right)\]
We know that, Perimeter of the rectangle \[\; = 2{\text{ }}(Length{\text{ }} + Breadth)\]
On putting the value in the above formula, we get
\[\begin{gathered}
  4\left( {x - 2} \right){\text{ }} = {\text{ }}2\left( {25{\text{ }} + {\text{ }}9} \right) \\
  4x{\text{ }}-{\text{ }}8{\text{ }} = {\text{ }}50{\text{ }} + {\text{ }}18 \\
  4x{\text{ }} = {\text{ }}76 \\
  X{\text{ }} = \dfrac{{76}}{4} = \;{\text{ }}19m \\
\end{gathered} \]
Therefore, x is \[19{\text{ }}m.\]

Note: Length or the rope used to measure the rectangle is the perimeter of the rectangle. Perimeter is the path that surrounds the figure or we can the outer boundary is called perimeter.