TV = 23.24
Solution:
Given STUV is a kite.
SV = 24, SW = 21.
To find the value of TV:
By the property of kite, diagonals bisect each other at right angles.
S, SWV is a right triangle.
Using Pythagoras theorem,
[tex]\text{Base} $^{2}+$ Height $^{2}=$ Hypotenuse $^{2}$[/tex]
[tex]\Rightarrow VW^2+SW^2=SV^2[/tex]
[tex]\Rightarrow VW^2+21^2=24^2[/tex]
[tex]\Rightarrow VW^2+441=576[/tex]
Subtract 441 from both sides of the equation.
[tex]\Rightarrow VW^2=135[/tex]
Taking square root on both sides of the equation.
[tex]\Rightarrow VW=3\sqrt{15}[/tex]
⇒ VW = 11.62
TV = 2 × VW
TV = 2 × 11.62
TV = 23.24
Hence the value of TV is 23.24.
