Question

Write the expression for the perimeter of a rectangle whose breadth is less than its length by 6 units.

Answer 1

Hint: Here we will assume the length of the rectangle to be x and then find the value of breadth in terms of x and then finally put the values in the formula for perimeter of the rectangle.
The perimeter of a rectangle is given by:-
\[P = 2\left( {l + b} \right)\] where l is the length of the rectangle and b is the breadth of the rectangle.

Complete step-by-step answer:
Let us assume the length of the rectangle to be x.
It is given that the breadth of the rectangle is less than its length by 6 units.
Therefore, the breadth is given by:-
\[b = x - 6\]
Now we know that the perimeter of a rectangle is given by:-
 \[P = 2\left( {l + b} \right)\]
Then putting in the respective values we get:-
\[P = 2\left( {x + x - 6} \right)\]
Solving it further we get:-
\[P = 2\left( {2x - 6} \right)\]
Simplifying it we get:-
\[P = 4x - 12\]

Hence the expression of perimeter is \[P = 4x - 12\] where x is the length of the rectangle.

Note: Students may also proceed by using the following method:-
Let the breadth of the rectangle be y.
Then it is given that the breadth of the rectangle is less than its length by 6 units.
This implies the length is 6 units more than the breadth.
Therefore, the length of the rectangle is given by:-
\[l = y + 6\]
Now we know that the perimeter of a rectangle is given by:-
 \[P = 2\left( {l + b} \right)\]
Then putting in the respective values we get:-
\[P = 2\left( {y + 6 + y} \right)\]
Solving it further we get:-
\[P = 2\left( {2y + 6} \right)\]
Simplifying it we get:-
\[P = 4y + 24\]
Hence the expression of perimeter is \[P = 4y + 24\] where y is the breadth of the rectangle.