question_answer

In fig. 1, ABCD is a rectangle. Find the values of x and y.

Answer:

Given, ABCD is a rectangle.

\[\therefore \]                  \[AB=CD\]

\[\Rightarrow \]               \[30=x+y\]

Or                     \[x+y=30\]

Similarly,           \[AD=BC\]                                                                    ?(i)

\[\Rightarrow \]               \[14=x-y\]

Or                  \[x-y=14\]

On adding eq. (i) and (ii), we get                                                               ?(ii)

\[2x=44\]

\[\Rightarrow \]               \[x=22\]

Putting the value of x in eq. (i), we get

\[22+y=30\]

\[\Rightarrow \]               \[y=30-22\]

\[\Rightarrow \]                 \[y=\text{ }8\]

So,  \[x=22,\text{ }y=8\].