Question

What is the parameter of a parallelogram with sides \[10{\text{ }}miles\] and \[1{\text{ }}mile?\]
A) \[20{\text{ }}mi\]
B) \[22{\text{ }}mi\]
C) \[21{\text{ }}mi\]
D) \[23{\text{ }}mi\]

Answer 1

Hint: Parallelogram is a type of quadrilateral that has equal and parallel opposite sides. So, to solve this problem we will first draw a figure where length of parallelogram will be equals to \[10{\text{ }}miles\] and breath will be equals to \[1{\text{ }}mile.\] Then by applying the formula of perimeter of parallelogram, and putting all the given values, we will get our required answer.

Complete step-by-step answer:
We have been given a parallelogram with sides \[10{\text{ }}miles\] and \[1{\text{ }}mile.\] We need to find the parameter of it.
So, let us draw a figure of a parallelogram using above details, i.e., length of parallelogram will be equals to \[10{\text{ }}miles\] and breath will be equals to \[1{\text{ }}mile.\] And then we will solve further.

Since, we know that parallelogram has equal and parallel opposite sides, so here side AB is parallel to side CD and side AD is parallel to side BC. Also, \[AD{\text{ }} = {\text{ }}BC{\text{ }} = {\text{ }}10{\text{ }}miles\] and \[AB{\text{ }} = {\text{ }}CD{\text{ }} = {\text{ }}1{\text{ }}mile.\]
Now, we know that, parameter of parallelogram
\[ = {\text{ }}AD{\text{ }} + {\text{ }}BC{\text{ }} + {\text{ }}AB{\text{ }} + {\text{ }}CD\]
On putting the values in the above formula, we get
\[
\Rightarrow {AD{\text{ }} + {\text{ }}AB{\text{ }} + {\text{ }}BC{\text{ }} + {\text{ }}CD{\text{ }} = {\text{ }}10{\text{ }}miles{\text{ }} + {\text{ }}1{\text{ }}mile{\text{ }} + {\text{ }}10{\text{ }}miles{\text{ }} + {\text{ }}1{\text{ }}mile} \\
{ = {\text{ }}22{\text{ }}miles.}
\]
So, the parameter of parallelogram is \[22{\text{ }}miles.\]

Thus, option (B) \[22{\text{ }}mi,\] is correct.

So, the correct answer is “Option B”.

Note: Let us know some facts or important properties about parallelograms. So, opposite sides of parallelograms are congruent. And opposite angles are also congruent. The consecutive angles of parallelogram are supplementary, i.e., equals to \[180^\circ .\] If one angle is the right angle, then all angles are the right angle. The diagonals of a parallelogram bisect each other. And each diagonal of a parallelogram separates it into two congruent triangles.