Question

The perimeter of a kite is 80 cm. If the length of one side is 20 cm, find the length of the other side.
A. 10 cm
B. 20 cm
C. 30 cm
D. none

Answer 1

Hint: We first form the shape of the kite and try to figure out the perimeter of the kite. We assume the breadth of the kite and put that in the equation of the perimeter of the quadrilateral. We get a linear equation of x and we solve it to find the solution to the problem.

Complete step-by-step solution
The shape of a kite is of the shape of a quadrilateral. It has two long sides and two short sides and consecutive two sides as a pair are equal.
It’s given that the perimeter of a kite is 80 cm. The length of one side is 20 cm. One consecutive side is also of length 20 cm.
Let’s assume that the other two sides of the quadrilateral are x cm.$(x>0)$.

Now we will try to find the perimeter of the kite.
We know that the perimeter is the sum of the sides which is $20+20+x+x$.
So, the perimeter of the kite is
$\begin{array}{rl}& 2(length+breadth)\\ & =2(20+x)\\ & =2x+40\end{array}$
Now we equate both sides to find the linear equation $2x+40=80$.
We solve the equation to find the value of x.
$\begin{array}{rl}& 2x+40=80\\ & \Rightarrow 2x=80-40=40\\ & \Rightarrow x={\displaystyle \frac{40}{2}}=20\end{array}$
The breadth of the kite is 20 cm. The correct option is B.

Note: We can see that the length and the breadth of the kite were both of the same lengths. So, the figure was more square-shaped rather than a rectangle. But it is not certain for every case and that’s why we can’t assume that the perimeter would be a square. Square is a special form of a rectangle.