The value of the other diagonal DF is 21.66 cm.
The top two sides measure 20 cm each and the bottom two sides measure 13 cm each.
One diagonal, EG, measures 24 cm.
The figure shows a kite in which all the dimensions are given.
Both the diagonals are perpendicular to each other since it is the diagonal of a kite. Diagonal ED divides the diagonal DF into two equal parts.
Therefore,
In triangle DOG, apply Pythagoras theorem, since it is a right triangle.
[tex]\begin{aligned}\left(\dfrac{x}{2} \right)^2+y^2&=13^2\\y^2&=169-\left(\dfrac{x}{2}\right)^2 \end{aligned}[/tex]
In triangle EOD, apply the Pythagoras theorem, since it is a right triangle.
[tex]\begin{aligned}\left(\dfrac{x}{2} \right)^2+(24-y)^2&=20^2\\\left(\dfrac{x}{2}\right)^2 +576-48y+y^2&=400\\\left(\dfrac{x}{2}\right)^2 +576-48y+169-\left(\dfrac{x}{2}\right)^2&=400\\-48y&=-345\\y&=7.1875\end{aligned}[/tex]
Substitute the value of y in the above expression and solve it for x.
[tex]\begin{aligned}7.1875 \times 7.1875&=169-\left(\dfrac{x}{2}\right)^2\\\left(\dfrac{x}{2}\right)^2&=169-51.6601\\\left(\dfrac{x}{2}\right)^2&=117.34\\\left(\dfrac{x}{2}\right)&=10.83\\x&=21.66\;\rm{cm} \end{aligned}[/tex]
Thus, the value of the other diagonal DF is 21.66 cm.
To know more about the kite shape, please refer to the link:
https://brainly.com/question/12231347
