Question

The perimeter of a kite is 40cm. What are the lengths of the other 3 sides, if the length of one of its sides is 15cm?

Answer 1

Hint: A kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other. So, use this concept to reach the solution of the given problem.

Complete step-by-step answer:
Since a kite has two equal pairs of equal sides. Let their sides be \[a\] and \[b\].
Perimeter can be defined as the path or boundary that surrounds a shape.
So, perimeter of a kite \[ = a + b + a + b = 2\left( {a + b} \right)\]
The diagram of kite is shown in the below figure:

Given perimeter of the kite is 40cm and one of its sides is equal to 15 cm i.e., let \[a = 15cm\]
$\Rightarrow 2\left( {a + b} \right) = 40 $
$   \Rightarrow 2\left( {15 + b} \right) = 40 $
Dividing both sides with 2, we get
 $  \Rightarrow 15 + b = 20 $
$   \Rightarrow b = 20 - 15 $
$  \therefore b = 5cm $
Since, a kite has two pairs of equal length sides, the sides of the kite are 15cm, 5cm, 15cm, 5cm.
Therefore, the other 3 sides of the kite are 5cm, 15cm, 5cm.

Note: The other properties of a kite are one pair of diagonally opposite angles is equal in measurement. These angles are said to be congruent with each other and the diagonals meet each other at right angles, this means that they form a perpendicular bisector.