Question

Fond the value of x and find the length of xy

Answer 1

From this Triangle

Taking Triangle XZH, wanting to find HZ

`\begin{gathered} We\text{ have to make use of pythgoras Theorem} \\ (XZ)^2=(XH)^2+(HZ)^2 \\ 12^2=8^2\text{ + }(HZ)^2 \\ 144\text{ = 64 + }(HZ)^2 \\ 144-64\text{ = }(HZ)^2 \\ (HZ)^2\text{ = 80} \\ (HZ)\text{ = }\sqrt[]{80\text{ }}\text{ =8.94} \\ \end{gathered}`

From the Second triangle, ZHY

`\begin{gathered} ZY^2=HZ^2+HY^2 \\ (x+3)^2\text{ =}8.94^2+x^2 \\ x^2+6x^{}\text{ + 9 = }80+x^2 \\ x^2-x^2\text{ + 6x = 80 -9} \\ 6x\text{ = 71} \\ x\text{ =}(71)/(6)\text{ =11.83} \\ \end{gathered}`

XY = x + 8

= 11.83 + 8

=19.83