❆ Cᴏɴᴄᴇᴘᴛ :-
In this question, we will take the help of the branch of mathematics known as "Perimeter and area". We will also use "linear equation in one variable". Let's solve it!
[tex] \sf \dag \: \red{Given :-}[/tex]
- Perimeter of a rectangle = 56 cm
Let the width be x
Therefore, the length will be 3x.
[tex] \sf \pink{Formula \: used :-} [/tex]
[tex] \boxed{ \red \bigstar \: { \sf \orange{perimeter \: of \: a \: rectangle \: = 2(length + breadth)}}} [/tex]
Now we will simply put the given values in the formula to get the required answer.
[tex] \sf \longrightarrow \: 56 \: cm = 2(x + 3x) \\ \sf \longrightarrow \: 56 \: cm = 2x + 6x \: \: \: \\ \sf \longrightarrow \: 8x = 56 \: cm \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \longrightarrow \: x = \frac{56 \: cm}{8} = 7 cm [/tex]
[tex] \sf \green{ \therefore \: width \: = x = 7 \: cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:} \\ \sf \green{ and \: length \: = 3x = 3 \times 7 = 21 \: cm}[/tex]
I hope that helps :))
