Question

The diagonal of a rectangular plot is 34 m and its perimeter is 92 m. Find its area.

Answer 1

Answer:

ar of rec =lb

perimeter of rec = 2(l+b)

Answer 2

Step-by-step explanation:

Let the length and width of the rectangular plot be x and y metres.

$\implies \: {x}^{2} + {y}^{2} = {(34)}^{2} \\{x}^{2} + {y}^{2} = 1156 .....(1) \\ perimeter \: of \: plot \: = 92 \: m \\ \implies \: 2(x + y) = 92 \\ x + y = \frac{92}{2} \\ x + y = 46 \\ squaring \: both \: sides: \\ (x + y)^{2} = (46)^{2} \\ {x}^{2} + {y}^{2} + 2xy = 2116........(2) \\ from \: equations \: (1) \: and \: (2) \\ 1156 + 2xy = 2116 \\ 2xy = 2116 - 1156 \\ 2xy = 960 \\ xy = \frac{960}{2} \\ xy = 480 \: {m}^{2} \\ thus \: the \: area \: of \: the \: rectangular \: \\ plot \: is \: 480 \: {m}^{2} .$