Question

Complete the above.

Answer 1

$$\textbf{Step 1: Find conditions by equating opposite sides of rectangle.}$$

$$\text{According to given diagram, we have}$$

$$2x + y + 8 = 4x - y$$

$$\Rightarrow 2x = 2y + 8$$

$$\Rightarrow x = y + 4$$ $$.......(1)$$

$$\text{Also,}$$

$$2y = x + 4$$ $$......(2)$$

$$\textbf{Step 2: Solve equations (1) and (2) using substitution method. }$$

$$\text{Substitute }x=y+4\text{ in equation (2), we get}$$

$$2y=(y+4)+4$$

$$y=8$$

$$\text{Substitute }y=8\text{ in equation (1), we get}$$

$$x=8+4=12$$

$$\Rightarrow y = 8 \ \ \& \ \ x = 12$$

$$\textbf{Step 3:Find the length and breadth of rectangle and then find perimeter and area of the rectangle.}$$

$$\text{Length}=l=4x-y=4(12)-8=40$$ $$[\because\boldsymbol{ y = 8 \ \ \& \ \ x = 12}]$$

$$\text{Breadth}=b=2y=2(8)=16$$ $$[\because\boldsymbol{ y = 8 \ \ \& \ \ x = 12}]$$

$$\text{Now,}$$

$$\text{Perimeter}= 2 ( 40 + 16)=112$$ $$[\because\textbf{Perimeter}\boldsymbol{= 2 ( l + b)}]$$

$$\text{Area}= 16 \times 40 = 640$$ $$\,[\because\textbf{Area}\boldsymbol{= l b}]$$

$$\textbf{Hence, perimeter and area of given rectangle are 112 and 640 respectively. }$$