Question

Find the values of the variables and the lengths of the sides of this kite. (image attached)thank you ! :)

Answer 1

Given:

Given that a kite having the lengths

`\begin{gathered} y-4 \\ x+5 \\ 2x+5 \\ x+12 \end{gathered}`

Required:

To find the value of the variable and the lengths of the sides of the kite.

Step-by-step explanation:

From the given figure

`\begin{gathered} 2x+5=x+12 \\ \\ 2x-x=12-5 \\ \\ x=7 \end{gathered}`

Now the length of the sides become

`\begin{gathered} 2x+5=2(7)+5 \\ =14+5 \\ =19 \end{gathered}`
`\begin{gathered} x+12=7+12 \\ =19 \end{gathered}`

And

`\begin{gathered} x+5=7+5 \\ =12 \end{gathered}`

Now the value of y is

`\begin{gathered} y-4=12 \\ y=12+4 \\ y=16 \end{gathered}`

Final Answer:

The value of variable is

`\begin{gathered} x=7 \\ y=16 \end{gathered}`

The sides lengths are 12,12,19 and 19.