We are given a kite in the given figure.
We need to find the the length of the kite’s longer diagonal.
Note: The diagonals of a kite cuts at right angle.
Therefore, we need to find the perpendicular sides of those right triangles formed.
For above small right triangle, base is 12 and hypotenuse is 13.
Applying Pythagoras theorem:
[tex]a^2 +b^2 = c^2[/tex]
12^2 +b^2 = 13^2
144 +b^2 = 169
b^2 = 169 - 144
b^2 = 25.
[tex]b= \sqrt{25}[/tex]
b=5.
For big right triangle, base is 12 and hypotenuse is 37.
Applying Pythagoras theorem:
12^2 + b^2 = 37^2
144 + b^2 = 1369
b^2 = 1369 - 144
b^2 = 1225
[tex]b = \sqrt{1225}[/tex]
b=35
Therefore, the length of the kite’s longer diagonal = 5 + 35 = 40 units.
