Hello, magentarita!
Is there a typo in the problem?
As stated, it has no solution.
The perimeter and the diagonal of a rectangle are 14m and 5m respectively.
Find its area. Code:
* - - - - - *
| * |
| *5 | W
| * |
* - - - - - *
L
The perimeter is 14: .$\displaystyle 2L + 2W = 14 \quad\Rightarrow\quad L + W \:=\:7$ .[1]
The diagonal is 5: .$\displaystyle L^2 + W^2 \:=\:5^2$ .[2] . . . (Pythagorus)
From [1], we have: .$\displaystyle W \:=\:7-L$
Substitute into [2]: .$\displaystyle L^2 + (7-L)^2 \:=\:25 \quad\Rightarrow\quad l^2-7L + 12 :=\:0$
Factor: .$\displaystyle (L-3)(L-4) \:=\:0 \quad\Rightarrow\quad L \;=\;3,\:4 \quad\Rightarrow\quad W \;=\;4,\:3$
The area is: .$\displaystyle 3 \times 4 \:=\:12\text{ m}^2$