The perimeter of kite OBDE is 38 units.
What is Pythagoras theorem?
Pythagoras theorem states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
What is perimeter?
Perimeter is the distance around the edge of a shape.
What is kite?
A kite is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.
According to the given question.
We have a circle with center o and diameter AB.
Triangle ABC is a right triangle.
To find the missing side, AB (which is the hypotenuse), we use the Pythagoras theorem.
So,
[tex](AB)^{2} = (10)^{2} +(24)^{2}[/tex]
[tex]\implies (AB)^{2} = 100+ 576\\\implies (AB)^{2} = 676\\\implies AB = \sqrt{676} \\\implies AB = 26[/tex]
Since, AB is the diameter of the circle. Therefore,
[tex]OB = \frac{AB}{2} \\\implies OB = \frac{26}{2} = 13[/tex]
Also, OBDE is a kite and we know that the adjacent sides of a kite are congruent.
[tex]\implies OB = BD = 13 \\\And,\ OE = ED = 6[/tex]
Therefore,
the perimeter of kite OBDE
= Length of sides (OB + BD + DE + EO )
= 13 + 13 + 6 + 6
= 26 + 12
= 38 units.
Hence, the perimeter of kite OBDE is 38 units.
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