Question

How would you translate word phrases to algebraic expressions: the perimeter of a rectangle with \[2n\] for the width and \[5n\] for the length?

Answer 1

Hint: To solve this question, we first need to observe the values provided to us. Forming an algebraic expression is easy here, because we already know the formula to find a rectangle’s perimeter. We have to put the values of width and length in the formula, and then derive the expression.

Complete step by step solution:
According to the question, we need to express the perimeter of a rectangle as an algebraic expression.
It is given that the width of the rectangle is \[2n\] , and the length of the rectangle is \[5n\] . We need to express the perimeter of the rectangle as an algebraic expression by using this information.
Now, the perimeter of a rectangle is actually \[2(l + b)\] , where \[l\] is the length, and \[b\] is the breadth of the rectangle.
By placing the values of width and length in the formula, we have the perimeter as \[2(2n + 5n)\] . On simplifying further, we will obtain \[2(7n)\] , which will ultimately result in \[14n\] .
Thus, the perimeter of a rectangle with \[2n\] for the width and \[5n\] for the length can be expressed as an algebraic expression, which is \[14n\] .
So, the correct answer is “ \[14n\] ”.

Note: Perimeter is essentially the continuous line forming the boundary of a closed geometric figure. All two-dimensional shapes have a perimeter, and for a rectangle, the perimeter equals the sum of lengths of all sides. This can be rewritten as the double of the sum of its length and width.