Question

Could someone help me with this problem? If STUV is a kite, SV=24, and SW=21, find TV.
(Round to the nearest tenth)

Answer 1

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,

$\text{Base} ^{2}+ Height ^{2}= Hypotenuse ^{2}$

$\Rightarrow VW^2+SW^2=SV^2$

$\Rightarrow VW^2+21^2=24^2$

$\Rightarrow VW^2+441=576$

Subtract 441 from both sides of the equation.

$\Rightarrow VW^2=135$

Taking square root on both sides of the equation.

$\Rightarrow VW=3\sqrt{15}$

⇒ VW = 11.62

TV = 2 × VW

TV = 2 × 11.62

TV = 23.24

Hence the value of TV is 23.24.