Question

The length of a rectangle is two times its breadth. Its perimeter is $60\mathrm{cm}$.(a) If the breadth of rectangle is $x\mathrm{cm}$, the length of the rectangle is _____ (b) Perimeter in terms of $x$ is _______ (c) The equation formed is _______ (d) The solution of the equation is ______

Answer 1

Step 1. Find the length of the rectangle.

It is given that the breadth of rectangle is $x\mathrm{cm}$ and length of a rectangle is two times its breadth.

Then, length of the rectangle is $2x$.

Step 2. Find the perimeter of the rectangle in terms of $x$.

Perimeter of rectangle is

$$\begin{gathered} =2(\mathrm{length}+\mathrm{breadth}) \\ =2\left(2x+x\right) \\ =2\times 3x \\ =6x \end{gathered}$$

Step 3. Find the equation formed.

Given perimeter is $60\mathrm{cm}$

The equation formed is, $4x+2x=60\mathrm{or}6\mathrm{x}=60$

Step 4. Find the solution of the equation .

The solution is

$$\begin{gathered} 6x=60 \\ \therefore x=10 \end{gathered}$$

Hence, the length of a rectangle is two times its breadth. Its perimeter is $60\mathrm{cm}$.(a) If the breadth of rectangle is $x\mathrm{cm}$, the length of the rectangle is $2x$ (b) Perimeter in terms of $x$ is $6x$ (c) The equation formed is $6x=60$ (d) The solution of the equation is $x=10$.