ABCD is rectagle . if AD is 14cm, AB is 30cm, BC is xy, DC is x+y then find the value of x and y.

Dear student,

$$\begin{gathered} Since ABCD is a rec\tan gle \\ \therefore its opposite sides will be equal \\ \Rightarrow AB=CD and AD=BC \\ \Rightarrow 30=x+y --\left(1\right) \\ and 14=xy --\left(2\right) \\ Solving the above 2 equation \\ x+y=30\Rightarrow x=30-y \\ Substitute the value of x in \left(2\right) \\ 14=\left(30-y\right)y \\ \Rightarrow 14=30y-y^2 \\ \Rightarrow y^2-30y+14=0 \\ u\sin g discriminate method \\ y=\frac{-(-30)\pm \sqrt{{\left(-30\right)}^2-4\times 1\times 14}}{2\times 1} \\ y=\frac{30\pm \sqrt{900-56}}{2} \\ y=\frac{30\pm \sqrt{844}}{2} \\ y=\frac{30\pm 29.051}{2} \\ Either y=\frac{30+29.051}{2} or y= \frac{30-29.051}{2} \\ y=\frac{59.051}{2}, or y= \frac{0.949}{2} \\ y=29.525, or y=0.474 \\ When y=29.52 then x=30-29.525=0.475 --[from 1] \\ and when y=0.474 then x=30-0.474=29.525 --[from 1] \end{gathered}$$
Note: Square root of 844 can be find out by long division method as shown below:-


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